Transmission method, transmission apparatus, reception method and reception apparatus

ABSTRACT

All data symbols used in data transmission of a modulated signal are precoded by hopping between precoding matrices so that the precoding matrix used to precode each data symbol and the precoding matrices used to precode data symbols that are adjacent to the data symbol in the frequency domain and the time domain all differ. A modulated signal with such data symbols arranged therein is transmitted.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims benefit to the U.S. provisional Application61/414,147, filed on Nov. 16, 2010.

BACKGROUND OF THE INVENTION

(1) Field of the Invention

The present invention relates to a precoding method, a precoding device,a transmission method, a transmission device, a reception method, and areception device that in particular perform communication using amulti-antenna.

(2) Description of the Related Art

Multiple-Input Multiple-Output (MIMO) is a conventional example of acommunication method using a multi-antenna. In multi-antennacommunication, of which MIMO is representative, multiple transmissionsignals are each modulated, and each modulated signal is transmittedfrom a different antenna simultaneously in order to increase thetransmission speed of data.

FIG. 28 shows an example of the structure of a transmission andreception device when the number of transmit antennas is two, the numberof receive antennas is two, and the number of modulated signals fortransmission (transmission streams) is two. In the transmission device,encoded data is interleaved, the interleaved data is modulated, andfrequency conversion and the like is performed to generate transmissionsignals, and the transmission signals are transmitted from antennas. Inthis case, the method for simultaneously transmitting differentmodulated signals from different transmit antennas at the same time andat the same frequency is spatial multiplexing MIMO.

In this context, it has been suggested in Patent Literature 1 to use atransmission device provided with a different interleave pattern foreach transmit antenna. In other words, the transmission device in FIG.28 would have two different interleave patterns with respectiveinterleaves (πa, πb). As shown in Non-Patent Literature 1 and Non-PatentLiterature 2, reception quality is improved in the reception device byiterative performance of a detection method that uses soft values (theMIMO detector in FIG. 28).

Models of actual propagation environments in wireless communicationsinclude non-line of sight (NLOS), of which a Rayleigh fading environmentis representative, and line of sight (LOS), of which a Rician fadingenvironment is representative. When the transmission device transmits asingle modulated signal, and the reception device performs maximal ratiocombining on the signals received by a plurality of antennas and thendemodulates and decodes the signal resulting from maximal ratiocombining, excellent reception quality can be achieved in an LOSenvironment, in particular in an environment where the Rician factor islarge, which indicates the ratio of the received power of direct wavesversus the received power of scattered waves. However, depending on thetransmission system (for example, spatial multiplexing MIMO system), aproblem occurs in that the reception quality deteriorates as the Ricianfactor increases (see Non-Patent Literature 3).

FIGS. 29A and 29B show an example of simulation results of the Bit ErrorRate (BER) characteristics (vertical axis: BER, horizontal axis:signal-to-noise power ratio (SNR)) for data encoded with low-densityparity-check (LDPC) code and transmitted over a 2×2 (two transmitantennas, two receive antennas) spatial multiplexing MIMO system in aRayleigh fading environment and in a Rician fading environment withRician factors of K=3, 10, and 16 dB. FIG. 29A shows the BERcharacteristics of Max-log A Posteriori Probability (APP) withoutiterative detection (see Non-Patent Literature 1 and Non-PatentLiterature 2), and FIG. 29B shows the BER characteristics of Max-log-APPwith iterative detection (see Non-Patent Literature 1 and Non-PatentLiterature 2) (number of iterations: five). As is clear from FIGS. 29Aand 29B, regardless of whether iterative detection is performed,reception quality degrades in the spatial multiplexing MIMO system asthe Rician factor increases. It is thus clear that the unique problem of“degradation of reception quality upon stabilization of the propagationenvironment in the spatial multiplexing MIMO system”, which does notexist in a conventional single modulation signal transmission system,occurs in the spatial multiplexing MIMO system.

Broadcast or multicast communication is a service directed towardsline-of-sight users. The radio wave propagation environment between thebroadcasting station and the reception devices belonging to the users isoften an LOS environment. When using a spatial multiplexing MIMO systemhaving the above problem for broadcast or multicast communication, asituation may occur in which the received electric field strength ishigh at the reception device, but degradation in reception quality makesit impossible to receive the service. In other words, in order to use aspatial multiplexing MIMO system in broadcast or multicast communicationin both an NLOS environment and an LOS environment, there is a desirefor development of a MIMO system that offers a certain degree ofreception quality.

Non-Patent Literature 8 describes a method to select a codebook used inprecoding (i.e. a precoding matrix, also referred to as a precodingweight matrix) based on feedback information from a communicationpartner. Non-Patent Literature 8 does not at all disclose, however, amethod for precoding in an environment in which feedback informationcannot be acquired from the communication partner, such as in the abovebroadcast or multicast communication.

On the other hand, Non-Patent Literature 4 discloses a method forswitching the precoding matrix over time. This method can be appliedeven when no feedback information is available. Non-Patent Literature 4discloses using a unitary matrix as the matrix for precoding andswitching the unitary matrix at random but does not at all disclose amethod applicable to degradation of reception quality in theabove-described LOS environment. Non-Patent Literature 4 simply reciteshopping between precoding matrices at random. Obviously, Non-PatentLiterature 4 makes no mention whatsoever of a precoding method, or astructure of a precoding matrix, for remedying degradation of receptionquality in an LOS environment.

CITATION LIST Patent Literature

-   Patent Literature 1-   WO 2005/050885

Non-Patent Literature

Non-Patent Literature 1

-   “Achieving near-capacity on a multiple-antenna channel”, IEEE    Transaction on Communications, vol. 51, no. 3, pp. 389-399, March    2003.

Non-Patent Literature 2

-   “Performance analysis and design optimization of LDPC-coded MIMO    OFDM systems”, IEEE Trans. Signal Processing, vol. 52, no. 2, pp.    348-361, February 2004.

Non-Patent Literature 3

-   “BER performance evaluation in 2×2 MIMO spatial multiplexing systems    under Rician fading channels”, IEICE Trans. Fundamentals, vol.    E91-A, no. 10, pp. 2798-2807, October 2008.

Non-Patent Literature 4

-   “Turbo space-time codes with time varying linear transformations”,    IEEE Trans. Wireless communications, vol. 6, no. 2, pp. 486-493,    February 2007.

Non-Patent Literature 5

-   “Likelihood function for QR-MLD suitable for soft-decision turbo    decoding and its performance”, IEICE Trans. Commun., vol. E88-B, no.    1, pp. 47-57, January 2004.

Non-Patent Literature 6

-   “A tutorial on ‘parallel concatenated (Turbo) coding’, ‘Turbo    (iterative) decoding’ and related topics”, The Institute of    Electronics, Information, and Communication Engineers, Technical    Report IT 98-51.

Non-Patent Literature 70

-   “Advanced signal processing for PLCs: Wavelet-OFDM”, Proc. of IEEE    International symposium on ISPLC 2008, pp. 187-192, 2008.

Non-Patent Literature 8

-   D. J. Love, and R. W. Heath, Jr., “Limited feedback unitary    precoding for spatial multiplexing systems”, IEEE Trans. Inf.    Theory, vol. 51, no. 8, pp. 2967-2976, August 2005.

Non-Patent Literature 9

-   DVB Document A122, Framing structure, channel coding and modulation    for a second generation digital terrestrial television broadcasting    system, (DVB-T2), June 2008.

Non-Patent Literature 10

-   L. Vangelista, N. Benvenuto, and S. Tomasin, “Key technologies for    next-generation terrestrial digital television standard DVB-T2”,    IEEE Commun. Magazine, vol. 47, no. 10, pp. 146-153, October 2009.

Non-Patent Literature 11

-   T. Ohgane, T. Nishimura, and Y. Ogawa, “Application of space    division multiplexing and those performance in a MIMO channel”,    IEICE Trans. Commun., vol. 88-B, no. 5, pp. 1843-1851, May 2005.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a MIMO system thatimproves reception quality in an LOS environment.

Solution to Problem

In order to solve the above problems, an aspect of the present inventionis a transmission method for transmitting a first transmission signalfrom one or more first outputs and a second transmission signal from oneor more second outputs that differ from the first outputs, the first andthe second transmission signal being generated by using one of aplurality of precoding matrices to precode a first and a secondmodulated signal modulated in accordance with a modulation method, thefirst and the second modulated signal being composed of an in-phasecomponent and a quadrature component, the precoding matrix used togenerate the first and the second transmission signal being regularlyswitched to another one of the precoding matrices, the transmissionmethod comprising the steps of: for a first symbol that is a data symbolused to transmit data of the first modulated signal and a second symbolthat is a data symbol used to transmit data of the second modulatedsignal, when a first time and a first frequency at which the firstsymbol is to be precoded and transmitted match a second time and asecond frequency at which the second symbol is to be precoded andtransmitted, two third symbols adjacent to the first symbol in thefrequency domain are both data symbols, and two fourth symbols adjacentto the first symbol in the time domain are both data symbols, generatingthe first transmission signal by precoding the first symbol, the twothird symbols, and the two fourth symbols, the first symbol beingprecoded with a different precoding matrix than each of the two thirdsymbols and the two fourth symbols; generating the second transmissionsignal by precoding the second symbol, two fifth symbols adjacent to thesecond symbol in the frequency domain, and two sixth symbols adjacent tothe second symbol in the time domain each with the same precoding matrixused to precode a symbol at a matching time and frequency among thefirst symbol, the two third symbols, and the two fourth symbols;outputting the generated first transmission signal from the one or morefirst outputs; and outputting the generated second transmission signalfrom the one or more second outputs.

Another aspect of the present invention is a transmission device fortransmitting a first transmission signal from one or more first outputsand a second transmission signal from one or more second outputs thatdiffer from the first outputs, the first and the second transmissionsignal being generated by using one of a plurality of precoding matricesto precode a first and a second modulated signal modulated in accordancewith a modulation method, the first and the second modulated signalbeing composed of an in-phase component and a quadrature component, theprecoding matrix used to generate the first and the second transmissionsignal being regularly switched to another one of the precodingmatrices, the transmission device comprising: a precoding weightgenerating unit operable to allocate precoding matrices, wherein for afirst symbol that is a data symbol used to transmit data of the firstmodulated signal and a second symbol that is a data symbol used totransmit data of the second modulated signal, when a first time and afirst frequency at which the first symbol is to be precoded andtransmitted match a second time and a second frequency at which a secondsymbol is to be precoded and transmitted, two third symbols adjacent tothe first symbol in the frequency domain are both data symbols, and twofourth symbols adjacent to the first symbol in the time domain are bothdata symbols, the precoding weight generating unit allocates precodingmatrices to the two third symbols and the two fourth symbols that differfrom the precoding matrix allocated to the first symbol, and allocatesthe same precoding matrix used to precode a symbol at a matching timeand frequency among the first symbol, the two third symbols, and the twofourth symbols to each of the second symbol, two fifth symbols adjacentto the second symbol in the frequency domain, and two sixth symbolsadjacent to the second symbol in the time domain; a weighting unitoperable to generate the first transmission signal and the secondtransmission signal by weighting the first modulated signal and thesecond modulated signal with the allocated precoding matrices; and atransmission unit operable to transmit the generated first transmissionsignal from the one or more first outputs and the generated secondtransmission signal from the one or more second outputs.

Another aspect of the present invention is a reception method forreceiving a first and a second transmission signal precoded andtransmitted by a transmission device, wherein the first and the secondtransmission signal are generated by using one of a plurality ofprecoding matrices, while regularly hopping between the precodingmatrices, to precode a first and a second modulated signal modulated inaccordance with a modulation method, the first and the second modulatedsignal being composed of an in-phase component and a quadraturecomponent, for a first symbol that is a data symbol used to transmitdata of the first modulated signal and a second symbol that is a datasymbol used to transmit data of the second modulated signal, when afirst time and a first frequency at which the first symbol is to beprecoded and transmitted match a second time and a second frequency atwhich the second symbol is to be precoded and transmitted, two thirdsymbols adjacent to the first symbol in the frequency domain are bothdata symbols, and two fourth symbols adjacent to the first symbol in thetime domain are both data symbols, then the first transmission signal isgenerated by precoding the first symbol, the two third symbols, and thetwo fourth symbols, the first symbol being precoded with a differentprecoding matrix than each of the two third symbols and the two fourthsymbols, and the second transmission signal is generated by precodingthe second symbol, two fifth symbols adjacent to the second symbol inthe frequency domain, and two sixth symbols adjacent to the secondsymbol in the time domain with the same precoding matrix used to precodea symbol at a matching time and frequency among the first symbol, thetwo third symbols, and the two fourth symbols, the reception methodcomprising the steps of: receiving the first and the second transmissionsignal; and demodulating the first and the second transmission signalusing a demodulation method in accordance with the modulation method andperforming error correction decoding to obtain data.

Another aspect of the present invention is a reception device forreceiving a first and a second transmission signal precoded andtransmitted by a transmission device, wherein the first and the secondtransmission signal are generated by using one of a plurality ofprecoding matrices, while regularly hopping between the precodingmatrices, to precode a first and a second modulated signal modulated inaccordance with a modulation method, the first and the second modulatedsignal being composed of an in-phase component and a quadraturecomponent, for a first symbol that is a data symbol used to transmitdata of the first modulated signal and a second symbol that is a datasymbol used to transmit data of the second modulated signal, when afirst time and a first frequency at which the first symbol is to beprecoded and transmitted match a second time and a second frequency atwhich the second symbol is to be precoded and transmitted, two thirdsymbols adjacent to the first symbol in the frequency domain are bothdata symbols, and two fourth symbols adjacent to the first symbol in thetime domain are both data symbols, then the first transmission signal isgenerated by precoding the first symbol, the two third symbols, and thetwo fourth symbols, the first symbol being precoded with a differentprecoding matrix than each of the two third symbols and the two fourthsymbols, the second transmission signal is generated by precoding thesecond symbol, two fifth symbols adjacent to the second symbol in thefrequency domain, and two sixth symbols adjacent to the second symbol inthe time domain with the same precoding matrix used to precode a symbolat a matching time and frequency among the first symbol, the two thirdsymbols, and the two fourth symbols, the first and the secondtransmission signal are received, and the first and the secondtransmission signal are demodulated using a demodulation method inaccordance with the modulation method and performing error correctiondecoding to obtain data.

With the above aspects of the present invention, a modulated signal isgenerated by performing precoding while hopping between precodingmatrices so that among a plurality of precoding matrices, a precodingmatrix used for at least one data symbol and precoding matrices that areused for data symbols that are adjacent to the data symbol in either thefrequency domain or the time domain all differ. Therefore, receptionquality in an LOS environment is improved in response to the design ofthe plurality of precoding matrices.

With the above structure, the present invention provides a transmissionmethod, a reception method, a transmission device, and a receptiondevice that remedy degradation of reception quality in an LOSenvironment, thereby providing high-quality service to LOS users duringbroadcast or multicast communication.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an example of the structure of a transmission device and areception device in a spatial multiplexing MIMO system.

FIG. 2 is an example of a frame structure.

FIG. 3 is an example of the structure of a transmission device whenadopting a method of hopping between precoding weights.

FIG. 4 is an example of the structure of a transmission device whenadopting a method of hopping between precoding weights.

FIG. 5 is an example of a frame structure.

FIG. 6 is an example of a method of hopping between precoding weights.

FIG. 7 is an example of the structure of a reception device.

FIG. 8 is an example of the structure of a signal processing unit in areception device.

FIG. 9 is an example of the structure of a signal processing unit in areception device.

FIG. 10 shows a decoding processing method.

FIG. 11 is an example of reception conditions.

FIGS. 12A and 12B are examples of BER characteristics.

FIG. 13 is an example of the structure of a transmission device whenadopting a method of hopping between precoding weights.

FIG. 14 is an example of the structure of a transmission device whenadopting a method of hopping between precoding weights.

FIGS. 15A and 15B are examples of a frame structure.

FIGS. 16A and 16B are examples of a frame structure.

FIGS. 17A and 17B are examples of a frame structure.

FIGS. 18A and 18B are examples of a frame structure.

FIGS. 19A and 19B are examples of a frame structure.

FIG. 20 shows positions of poor reception quality points.

FIG. 21 shows positions of poor reception quality points.

FIG. 22 is an example of a frame structure.

FIG. 23 is an example of a frame structure.

FIGS. 24A and 24B are examples of mapping methods.

FIGS. 25A and 25B are examples of mapping methods.

FIG. 26 is an example of the structure of a weighting unit.

FIG. 27 is an example of a method for reordering symbols.

FIG. 28 is an example of the structure of a transmission device and areception device in a spatial multiplexing MIMO system.

FIGS. 29A and 29B are examples of BER characteristics.

FIG. 30 is an example of a 2×2 MIMO spatial multiplexing MIMO system.

FIGS. 31A and 31B show positions of poor reception points.

FIG. 32 shows positions of poor reception points.

FIGS. 33A and 33B show positions of poor reception points.

FIG. 34 shows positions of poor reception points.

FIGS. 35A and 35B show positions of poor reception points.

FIG. 36 shows an example of minimum distance characteristics of poorreception points in an imaginary plane.

FIG. 37 shows an example of minimum distance characteristics of poorreception points in an imaginary plane.

FIGS. 38A and 38B show positions of poor reception points.

FIGS. 39A and 39B show positions of poor reception points.

FIG. 40 is an example of the structure of a transmission device inEmbodiment 7.

FIG. 41 is an example of the frame structure of a modulated signaltransmitted by the transmission device.

FIGS. 42A and 42B show positions of poor reception points.

FIGS. 43A and 43B show positions of poor reception points.

FIGS. 44A and 44B show positions of poor reception points.

FIGS. 45A and 45B show positions of poor reception points.

FIGS. 46A and 46B show positions of poor reception points.

FIGS. 47A and 47B are examples of a frame structure in the time andfrequency domains.

FIGS. 48A and 48B are examples of a frame structure in the time andfrequency domains.

FIG. 49 shows a signal processing method.

FIG. 50 shows the structure of modulated signals when using space-timeblock coding.

FIG. 51 is a detailed example of a frame structure in the time andfrequency domains.

FIG. 52 is an example of the structure of a transmission device.

FIG. 53 is an example of a structure of the modulated signal generatingunits #1-#M in FIG. 52.

FIG. 54 shows the structure of the OFDM related processors (5207_1 and5207_2) in FIG. 52.

FIGS. 55A and 55B are detailed examples of a frame structure in the timeand frequency domains.

FIG. 56 is an example of the structure of a reception device.

FIG. 57 shows the structure of the OFDM related processors (5600_X and5600_Y) in FIG. 56.

FIGS. 58A and 58B are detailed examples of a frame structure in the timeand frequency domains.

FIG. 59 is an example of a broadcasting system.

FIGS. 60A and 60B show positions of poor reception points.

FIGS. 61A and 61B are examples of frame structure of a modulated signalyielding high reception quality.

FIGS. 62A and 62B are examples of frame structure of a modulated signalnot yielding high reception quality.

FIGS. 63A and 63B are examples of symbol arrangement of a modulatedsignal yielding high reception quality.

FIGS. 64A and 64B are examples of symbol arrangement of a modulatedsignal yielding high reception quality.

FIGS. 65A and 65B are examples of symbol arrangement in which thefrequency domain and the time domain in the examples of symbolarrangement in FIGS. 63A and 63B are switched.

FIGS. 66A and 66B are examples of symbol arrangement in which thefrequency domain and the time domain in the examples of symbolarrangement in FIGS. 64A and 64B are switched.

FIGS. 67A, 67B, 67C, and 67D show examples of the order of symbolarrangement.

FIGS. 68A, 68B, 68C, and 68D show examples of symbol arrangement whenpilot symbols are not inserted between data symbols.

FIGS. 69A and 69B show insertion of pilot symbols between data symbols.

FIGS. 70A and 70B are examples of symbol arrangement showing locationswhere a symbols arrangement yielding high reception quality cannot beachieved when pilot symbols are simply inserted.

FIGS. 71A and 71B show examples of symbol arrangement when pilot symbolsare inserted between data symbols.

FIGS. 72A and 72B are examples of frame structure of a modulated signalyielding high reception quality wherein the range over which precodingmatrices differ is expanded.

FIGS. 73A and 73B are examples of frame structure of a modulated signalyielding high reception quality wherein the range over which precodingmatrices differ is expanded.

FIGS. 74A and 74B are examples of symbol arrangement wherein the rangeover which precoding matrices differ is expanded.

FIGS. 75A and 75B are examples of frame structure of a modulated signalyielding high reception quality wherein the range over which precodingmatrices differ is expanded.

FIGS. 76A and 76B are examples, corresponding to FIGS. 75A and 75B, ofsymbol arrangement yielding high reception quality.

FIGS. 77A and 77B are examples of frame structure of a modulated signalyielding high reception quality wherein the range over which precodingmatrices differ is expanded.

FIGS. 78A and 78B are examples, corresponding to FIGS. 77A and 77B, ofsymbol arrangement yielding high reception quality.

FIGS. 79A and 79B are examples of symbol arrangement wherein the rangeover which precoding matrices differ is expanded and pilot symbols areinserted between data symbols.

FIGS. 80A and 80B are examples of symbol arrangement in which adifferent method of allocating precoding matrices than FIGS. 70A and 70Bis used.

FIGS. 81A and 81B are examples of symbol arrangement in which adifferent method of allocating precoding matrices than FIGS. 70A and 70Bis used.

FIG. 82 shows the overall structure of a digital broadcasting system.

FIG. 83 is a block diagram showing an example of the structure of areception device.

FIG. 84 shows the structure of multiplexed data.

FIG. 85 schematically shows how each stream is multiplexed in themultiplexed data.

FIG. 86 shows in detail how a video stream is stored in a sequence ofPES packets.

FIG. 87 shows the structure of a TS packet and a source packet inmultiplexed data.

FIG. 88 shows the data structure of a PMT.

FIG. 89 shows the internal structure of multiplexed data information.

FIG. 90 shows the internal structure of stream attribute information.

FIG. 91 is a structural diagram of a video display and an audio outputdevice.

DESCRIPTION OF EMBODIMENTS

The following describes embodiments of the present invention withreference to the drawings.

Embodiment 1

The following describes the transmission method, transmission device,reception method, and reception device of the present embodiment.

Prior to describing the present embodiment, an overview is provided of atransmission method and decoding method in a conventional spatialmultiplexing MIMO system.

FIG. 1 shows the structure of an N_(t)×N_(r) spatial multiplexing MIMOsystem. An information vector z is encoded and interleaved. As output ofthe interleaving, an encoded bit vector u=(u₁, . . . , u_(m)) isacquired. Note that u_(i)=(u_(i1), . . . , u_(iM)) (where M is thenumber of transmission bits per symbol). Letting the transmission vectors=(s₁, . . . , s_(Nt))^(T) and the transmission signal from transmitantenna #1 be represented as s_(i)=map(u_(i)), the normalizedtransmission energy is represented as E{|s_(i)|²}=Es/Nt (E_(s) being thetotal energy per channel). Furthermore, letting the received vector bey=(y₁, . . . , y_(Nr))^(T), the received vector is represented as inEquation 1.

$\begin{matrix}{{Math}\mspace{14mu} 1} & \; \\\begin{matrix}{y = \left( {y_{1},\ldots\mspace{11mu},y_{Nr}} \right)^{T}} \\{= {{H_{NtNr}s} + n}}\end{matrix} & {{Equation}\mspace{14mu} 1}\end{matrix}$

In this Equation, H_(NtNr) is the channel matrix, n=(n₁, . . . ,n_(Nr))^(T) is the noise vector, and n_(i) is the i.i.d. complexGaussian random noise with an average value 0 and variance σ². From therelationship between transmission symbols and reception symbols that isinduced at the reception device, the probability for the received vectormay be provided as a multi-dimensional Gaussian distribution, as inEquation 2.

$\begin{matrix}{{Math}\mspace{14mu} 2} & \; \\{{p\left( y \middle| u \right)} = {\frac{1}{\left( {2\;\pi\;\sigma^{2}} \right)^{N,}}{\exp\left( {{- \frac{1}{2\;\sigma^{2}}}{{y - {{Hs}(u)}}}^{2}} \right)}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

Here, a reception device that performs iterative decoding composed of anouter soft-in/soft-out decoder and a MIMO detector, as in FIG. 1, isconsidered. The vector of a log-likelihood ratio (L-value) in FIG. 1 isrepresented as in Equations 3-5.

$\begin{matrix}{{Math}\mspace{14mu} 3} & \; \\{{L(u)} = \left( {{L\left( u_{1} \right)},\ldots\mspace{11mu},{L\left( u_{N_{t}} \right)}} \right)^{T}} & {{Equation}\mspace{14mu} 3} \\{{Math}\mspace{14mu} 4} & \; \\{{L\left( u_{i} \right)} = \left( {{L\left( u_{i\; 1} \right)},\ldots\mspace{11mu},{L\left( u_{iM} \right)}} \right)} & {{Equation}\mspace{14mu} 4} \\{{Math}\mspace{14mu} 5} & \; \\{{L\left( u_{ij} \right)} = {\ln\frac{P\left( {u_{ij} = {+ 1}} \right)}{P\left( {u_{ij} = {- 1}} \right)}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$<Iterative Detection Method>

The following describes iterative detection of MIMO signals in theN_(t)×N_(r) spatial multiplexing MIMO system.

The log-likelihood ratio of u_(mn) is defined as in Equation 6.

$\begin{matrix}{{Math}\mspace{14mu} 6} & \; \\{{L\left( u_{mn} \middle| y \right)} = {\ln\frac{P\left( {u_{mn} = \left. {+ 1} \middle| y \right.} \right)}{P\left( {u_{mn} = \left. {- 1} \middle| y \right.} \right)}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

From Bayes' theorem, Equation 6 can be expressed as Equation 7.

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 7}} & \; \\\begin{matrix}{{L\left( u_{mn} \middle| y \right)} = {\ln\frac{{p\left( {\left. y \middle| u_{mn} \right. = {+ 1}} \right)}{{P\left( {u_{mn} = {+ 1}} \right)}/{p(y)}}}{{p\left( {\left. y \middle| u_{mn} \right. = {- 1}} \right)}{{P\left( {u_{mn} = {- 1}} \right)}/{p(y)}}}}} \\{= {{\ln\frac{P\left( {u_{mn} = {+ 1}} \right)}{P\left( {u_{mn} = {- 1}} \right)}} + {\ln\frac{p\left( {\left. y \middle| u_{mn} \right. = {+ 1}} \right)}{p\left( {\left. y \middle| u_{mn} \right. = {- 1}} \right)}}}} \\{= {{\ln\frac{P\left( {u_{mn} = {+ 1}} \right)}{P\left( {u_{mn} = {- 1}} \right)}} + {\ln\frac{\sum_{U_{{mn},{+ 1}}}{{p\left( y \middle| u \right)}{p\left( u \middle| u_{mn} \right)}}}{\sum_{U_{{mn},{- 1}}}{{p\left( y \middle| u \right)}{p\left( u \middle| u_{mn} \right)}}}}}}\end{matrix} & {{Equation}\mspace{14mu} 7}\end{matrix}$

Let U_(mn,±1)={u|u_(mn)=±1}. When approximating ln Σa_(j)˜max ln a_(j),an approximation of Equation 7 can be sought as Equation 8. Note thatthe above symbol “˜” indicates approximation.

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 8}} & \; \\{{L\left( {u_{mn}❘y} \right)} \approx {{\ln\frac{P\left( {u_{mn} = {+ 1}} \right)}{P\left( {u_{mn} = {- 1}} \right)}} + {\max\limits_{{Umn},{+ 1}}\left\{ {{\ln\;{p\left( {y❘u} \right)}} + {P\left( {u❘u_{mn}} \right)}} \right\}} - {\max\limits_{{Umn},{- 1}}\left\{ {{\ln\;{p\left( {y❘u} \right)}} + {P\left( {u❘u_{mn}} \right)}} \right\}}}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

P(u|u_(mn)) and ln P(u|u_(mn)) in Equation 8 are represented as follows.

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 9}} & \; \\\begin{matrix}{\mspace{79mu}{{P\left( {u❘u_{mn}} \right)} = {\prod\limits_{{({ij})} \neq {({mn})}}\;{P\left( u_{ij} \right)}}}} \\{= {\prod\limits_{{({ij})} \neq {({mn})}}\frac{\exp\left( \frac{u_{ij}{L\left( u_{ij} \right)}}{2} \right)}{{\exp\left( \frac{L\left( u_{ij} \right)}{2} \right)} + {\exp\left( {- \frac{L\left( u_{ij} \right)}{2}} \right)}}}}\end{matrix} & {{Equation}\mspace{14mu} 9} \\{\mspace{79mu}{{Math}\mspace{14mu} 10}} & \; \\{\mspace{79mu}{{\ln\;{P\left( {u❘u_{mn}} \right)}} = {\left( {\sum\limits_{ij}{\ln\;{P\left( u_{ij} \right)}}} \right) - {\ln\;{P\left( u_{mn} \right)}}}}} & {{Equation}\mspace{14mu} 10} \\{\mspace{79mu}{{Math}\mspace{14mu} 11}} & \; \\\begin{matrix}{{\ln\;{P\left( u_{ij} \right)}} = {{\frac{1}{2}u_{ij}{P\left( u_{ij} \right)}} - {\ln\left( {{\exp\left( \frac{L\left( u_{ij} \right)}{2} \right)} + {\exp\left( {- \frac{L\left( u_{ij} \right)}{2}} \right)}} \right)}}} \\{\approx {{\frac{1}{2}u_{ij}{L\left( u_{ij} \right)}} - {\frac{1}{2}{{L\left( u_{ij} \right)}}\mspace{14mu}{for}\mspace{14mu}{{L\left( u_{ij} \right)}}}} > 2} \\{= {{\frac{L\left( u_{ij} \right)}{2}}\left( {{u_{ij}{{sign}\left( {L\left( u_{ij} \right)} \right)}} - 1} \right)}}\end{matrix} & {{Equation}\mspace{14mu} 11}\end{matrix}$

Incidentally, the logarithmic probability of the equation defined inEquation 2 is represented in Equation 12.

$\begin{matrix}{{Math}\mspace{14mu} 12} & \; \\{{\ln\;{P\left( {y❘u} \right)}} = {{{- \frac{N_{r}}{2}}{\ln\left( {2\;\pi\;\sigma^{2}} \right)}} - {\frac{1}{2\;\sigma^{2}}{{y - {{Hs}(u)}}}^{2}}}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

Accordingly, from Equations 7 and 13, in MAP or A Posteriori Probability(APP), the a posteriori L-value is represented as follows.

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 13}} & \; \\{{L\left( {u_{mn}❘y} \right)} = {\ln\frac{\sum\limits_{U_{{mn},{+ 1}}}{\exp\left\{ {{{- \frac{1}{2\;\sigma^{2}}}{{y - {{Hs}(u)}}}^{2}} + {\sum\limits_{ij}{\ln\;{P\left( u_{ij} \right)}}}} \right\}}}{\sum\limits_{U_{{mn},{- 1}}}{\exp\left\{ {{{- \frac{1}{2\;\sigma^{2}}}{{y - {{Hs}(u)}}}^{2}} + {\sum\limits_{ij}{\ln\;{P\left( u_{ij} \right)}}}} \right\}}}}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

Hereinafter, this is referred to as iterative APP decoding. FromEquations 8 and 12, in the log-likelihood ratio utilizing Max-Logapproximation (Max-Log APP), the a posteriori L-value is represented asfollows.

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 14}} & \; \\{{L\left( {u_{mn}❘y} \right)} \approx {{\max\limits_{{Umn},{+ 1}}\left\{ {\Psi\left( {u,y,{L(u)}} \right)} \right\}} - {\max\limits_{{Umn},{- 1}}\left\{ {\Psi\left( {u,y,{L(u)}} \right)} \right\}}}} & {{Equation}\mspace{14mu} 14} \\{\mspace{79mu}{{Math}\mspace{14mu} 15}} & \; \\{\mspace{79mu}{{\Psi\left( {u,y,{L(u)}} \right)} = {{{- \frac{1}{2\;\sigma^{2}}}{{y - {{Hs}(u)}}}^{2}} + {\sum\limits_{ij}{\ln\;{P\left( u_{ij} \right)}}}}}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

Hereinafter, this is referred to as iterative Max-log APP decoding. Theextrinsic information required in an iterative decoding system can besought by subtracting prior inputs from Equations 13 and 14.

<System Model>

FIG. 28 shows the basic structure of the system that is related to thesubsequent description. This system is a 2×2 spatial multiplexing MIMOsystem. There is an outer encoder for each of streams A and B. The twoouter encoders are identical LDPC encoders. (Here, a structure usingLDPC encoders as the outer encoders is described as an example, but theerror correction coding used by the outer encoder is not limited to LDPCcoding. The present invention may similarly be embodied using othererror correction coding such as turbo coding, convolutional coding, LDPCconvolutional coding, and the like. Furthermore, each outer encoder isdescribed as having a transmit antenna, but the outer encoders are notlimited to this structure. A plurality of transmit antennas may be used,and the number of outer encoders may be one. Also, a greater number ofouter encoders may be used than the number of transmit antennas.) Thestreams A and B respectively have interleavers (π_(a), π_(b)). Here, themodulation scheme is 2^(h)-QAM (with h bits transmitted in one symbol).

The reception device performs iterative detection on the above MIMOsignals (iterative APP (or iterative Max-log APP) decoding). Decoding ofLDPC codes is performed by, for example, sum-product decoding.

FIG. 2 shows a frame structure and lists the order of symbols afterinterleaving. In this case, (i_(a), j_(a)), (i_(b), j_(b)) arerepresented by the following Equations.Math 16(i _(a) ,j _(a))=π_(a)(Ω_(ia,ja) ^(a))  Equation 16Math 17(i _(b) ,j _(b))=π_(b)(Ω_(ib,jb) ^(a))  Equation 17

In this case, i^(a), i^(b) indicate the order of symbols afterinterleaving, j^(a), j^(b) indicate the bit positions (j^(a), j^(b)=1, .. . , h) in the modulation scheme, π^(a), π^(b) indicate theinterleavers for the streams A and B, and Ω_(ia,ja) ^(a), Ω_(ib,jb) ^(b)indicate the order of data in streams A and B before interleaving. Notethat FIG. 2 shows the frame structure for i_(a)=i_(b).

<Iterative Decoding>

The following is a detailed description of the algorithms forsum-product decoding used in decoding of LDPC codes and for iterativedetection of MIMO signals in the reception device.

Sum-Product Decoding

Let a two-dimensional M×N matrix H={H_(mn)} be the check matrix for LDPCcodes that are targeted for decoding. Subsets A(m), B(n) of the set [1,N]={1, 2, . . . , N} are defined by the following Equations.Math 18A(m)≡{n:H _(mn)=1}  Equation 18Math 19B(m)≡{m:H _(mn)=1}  Equation 19

In these Equations, A(m) represents the set of column indices of 1 's inthe m^(th) column of the check matrix H, and B(n) represents the set ofrow indices of 1's in the n^(th) row of the check matrix H. Thealgorithm for sum-product decoding is as follows.

Step A•1 (initialization): let a priori value logarithmic ratio β_(mn)=0for all combinations (m, n) satisfying H_(mn)=1. Assume that the loopvariable (the number of iterations) l_(sum)=1 and the maximum number ofloops is set to l_(sum, max).

Step A•2 (row processing): the extrinsic value logarithmic ratio α_(mn)is updated for all combinations (m, n) satisfying H_(mn)=1 in the orderof m=1, 2, . . . , M, using the following updating Equations.

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 20}} & \; \\{\alpha_{mn} = {\left( {\prod\limits_{n^{\prime} \in {{A{(m)}} \smallsetminus n}}\;{{sign}\left( {\lambda_{n^{\prime}} + \beta_{{mn}^{\prime}}} \right)}} \right) \times {f\left( {\sum\limits_{n^{\prime} \in {{A{(m)}} \smallsetminus n}}{f\left( {\lambda_{n^{\prime}} + \beta_{{mn}^{\prime}}} \right)}} \right)}}} & {{Equation}\mspace{14mu} 20} \\{\mspace{79mu}{{Math}\mspace{14mu} 21}} & \; \\{\mspace{85mu}{{{sign}(x)} \equiv \left\{ \begin{matrix}1 & {x \geq 0} \\{- 1} & {x < 0}\end{matrix} \right.}} & {{Equation}\mspace{14mu} 21} \\{\mspace{79mu}{{Math}\mspace{14mu} 22}} & \; \\{\mspace{79mu}{{f(x)} \equiv {\ln\frac{{\exp(x)} + 1}{{\exp(x)} - 1}}}} & {{Equation}\mspace{14mu} 22}\end{matrix}$

In these Equations, f represents a Gallager function. Furthermore, themethod of seeking λ_(n) is described in detail later.

Step A•3 (column processing): the extrinsic value logarithmic ratioβ_(mn) is updated for all combinations (m, n) satisfying H_(mn)=1 in theorder of n=1, 2, . . . , N, using the following updating Equation.

$\begin{matrix}{{Math}\mspace{14mu} 23} & \; \\{\beta_{mn} = {\sum\limits_{m^{\prime} \in {{B{(n)}} \smallsetminus m}}\alpha_{m^{\prime}n}}} & {{Equation}\mspace{14mu} 23}\end{matrix}$Step A•4 (calculating a log-likelihood ratio): the log-likelihood ratioL_(n) is sought for nε[1, N] by the following Equation.

$\begin{matrix}{{Math}{\mspace{14mu}\;}23} & \; \\{L_{n} = {{\sum\limits_{m^{\prime} \in {{B{(n)}}\backslash m}}\;\alpha_{m^{\prime}n}} + \lambda_{n}}} & {{Equation}\mspace{14mu} 24}\end{matrix}$Step A•5 (count of the number of iterations): if l_(sum)<l_(sum, max)then l_(sum) is incremented, and processing returns to step A2. Ifl_(sum)=l_(sum, max), the sum-product decoding in this round isfinished.

The operations in one sum-product decoding have been described.Subsequently, iterative MIMO signal detection is performed. In thevariables m, n, α_(mn), β_(mn), λ_(n), and L_(n), used in the abovedescription of the operations of sum-product decoding, the variables instream A are m_(a), n_(a), α_(mana) ^(a), β_(mana) ^(a), λ_(na) andL_(na), and the variables in stream B are m_(b), n_(b), α_(mbnb) ^(b),β_(mbnb) ^(b), λ_(nb) and L_(nb).

<Iterative MIMO Signal Detection>

The following describes the method of seeking λ_(n) in iterative MIMOsignal detection in detail.

The following Equation holds from Equation 1.

$\begin{matrix}{{Math}\mspace{14mu} 25} & \; \\\begin{matrix}{{y(t)} = \left( {{y_{1}(t)},{y_{2}(t)}} \right)^{T}} \\{= {{{H_{22}(t)}{s(t)}} + {n(t)}}}\end{matrix} & {{Equation}\mspace{14mu} 25}\end{matrix}$

The following Equations are defined from the frame structures of FIG. 2and from Equations 16 and 17.Math 26n _(a)=Ω_(ia,ja) ^(a)  Equation 26Math 27n _(b)=Ω_(ib,jb) ^(b)  Equation 27

In this case, n_(a),n_(b) ε[1, N]. Hereinafter, λ_(na), L_(na), λ_(nb),and L_(nb), where the number of iterations of iterative MIMO signaldetection is k, are represented as λ_(k,na), L_(k,na), λ_(k,nb) andL_(k,nb).

Step B•1 (initial detection; k=0): λ_(0,na) and λ_(0,nb) are sought asfollows in the case of initial detection.

In iterative APP decoding:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 28}} & \; \\{\lambda_{0,_{n_{X}}} = {\ln\frac{\sum\limits_{U_{0,_{n_{X},}{+ 1}}}{\exp\left\{ {{- \frac{1}{2\;\sigma^{2}}}{{{y\left( i_{X} \right)} - {{H_{22}\left( i_{X} \right)}{s\left( {u\left( i_{X} \right)} \right)}}}}^{2}} \right\}}}{\sum\limits_{U_{0,_{n_{X},}{- 1}}}{\exp\left\{ {{- \frac{1}{2\;\sigma^{2}}}{{{y\left( i_{X} \right)} - {{H_{22}\left( i_{X} \right)}{s\left( {u\left( i_{X} \right)} \right)}}}}^{2}} \right\}}}}} & {{Equation}\mspace{14mu} 28}\end{matrix}$

In iterative Max-log APP decoding:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 29}} & \; \\{\lambda_{0,_{n_{X}}} = {{\max\limits_{U_{0,_{n_{X},}{+ 1}}}\left\{ {\Psi\left( {{u\left( i_{X} \right)},{y\left( i_{X} \right)}} \right)} \right\}} - {\max\limits_{U_{0,_{n_{X},}{- 1}}}\left\{ {\Psi\left( {{u\left( i_{X} \right)},{y\left( i_{X} \right)}} \right)} \right\}}}} & {{Equation}\mspace{14mu} 29} \\{\mspace{79mu}{{Math}\mspace{14mu} 30}} & \; \\{\mspace{79mu}{{\Psi\left( {{u\left( i_{X} \right)},{y\left( i_{X} \right)}} \right)} = {{- \frac{1}{2\;\sigma^{2}}}{{{y\left( i_{X} \right)} - {{H_{22}\left( i_{X} \right)}{s\left( {u\left( i_{X} \right)} \right)}}}}^{2}}}} & {{Equation}\mspace{14mu} 30}\end{matrix}$

Here, let X=a, b. Then, assume that the number of iterations ofiterative MIMO signal detection is l_(mimo) and the maximum number ofiterations is set to l_(mimo,max).

Step B•2 (iterative detection; the number of iterations k) λ_(k,na) andλ_(k,nb), where the number of iterations is k, are represented as inEquations 31-34, from Equations 11, 13-15, 16, and 17. Let (X, Y)=(a,b)(b, a).

In iterative APP decoding:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 31}} & \; \\{\lambda_{k,_{n_{X}}} = {{L_{{k - 1},\Omega_{{iX},{jX}}^{X}}\left( u_{\Omega_{{iX},{jX}}^{X}} \right)} + {\ln\frac{\sum\limits_{U_{k,_{n_{X}},{+ 1}}}{\exp\begin{Bmatrix}{{{- \frac{1}{2\;\sigma^{2}}}{{{y\left( i_{X} \right)} - {{H_{22}\left( i_{X} \right)}{s\left( {u\left( i_{X} \right)} \right)}}}}^{2}} +} \\{\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)}\end{Bmatrix}}}{\sum\limits_{U_{k,_{n_{X}},{- 1}}}{\exp\begin{Bmatrix}{{{- \frac{1}{2\;\sigma^{2}}}{{{y\left( i_{X} \right)} - {{H_{22}\left( i_{X} \right)}{s\left( {u\left( i_{X} \right)} \right)}}}}^{2}} +} \\{\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)}\end{Bmatrix}}}}}} & {{Equation}\mspace{14mu} 31} \\{\mspace{79mu}{{Math}\mspace{14mu} 32}} & \; \\{{\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)} = {{\sum\limits_{\underset{\gamma \neq {jX}}{\gamma = 1}}^{h}{{\frac{L_{{k - 1},\Omega_{{iX},\gamma}^{X}}\left( u_{\Omega_{{iX},\gamma}^{X}} \right)}{2}}\left( {{u_{\Omega_{{iX},\gamma}^{X}}{{sign}\left( {L_{{k - 1},\Omega_{{iX},\gamma}^{X}}\left( u_{\Omega_{{iX},\gamma}^{X}} \right)} \right)}} - 1} \right)}} + {\sum\limits_{\gamma = 1}^{h}{{\frac{L_{{k - 1},\Omega_{{iX},\gamma}^{X}}\left( u_{\Omega_{{iX},\gamma}^{X}} \right)}{2}}\left( {{u_{\Omega_{{iX},\gamma}^{X}}{{sign}\left( {L_{{k - 1},\Omega_{{iX},\gamma}^{X}}\left( u_{\Omega_{{iX},\gamma}^{X}} \right)} \right)}} - 1} \right)}}}} & {{Equation}\mspace{14mu} 32}\end{matrix}$

In iterative Max-log APP decoding:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 33}} & \; \\{\lambda_{k,_{n_{X}}} = {{L_{{k - 1},\Omega_{{iX},{jX}}^{X}}\left( u_{\Omega_{{iX},{jX}}^{X}} \right)} + {\max\limits_{U_{k,n_{X},{+ 1}}}\left\{ {\Psi\left( {{u\left( i_{X} \right)},{y\left( i_{X} \right)},{\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)}} \right)} \right\}} - {\max\limits_{U_{k,n_{X},{- 1}}}\left\{ {\Psi\left( {{u\left( i_{X} \right)},{y\left( i_{X} \right)},{\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)}} \right)} \right\}}}} & {{Equation}\mspace{14mu} 33} \\{\mspace{79mu}{{Math}\mspace{14mu} 34}} & \; \\{{\Psi\left( {{u\left( i_{X} \right)},{y\left( i_{X} \right)},{\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)}} \right)} = {{{- \frac{1}{2\;\sigma^{2}}}{{{y\left( i_{X} \right)} - {{H_{22}\left( i_{X} \right)}{s\left( {u\left( i_{X} \right)} \right)}}}}^{2}} + {\rho\left( u_{\Omega_{{iX},{jX}}^{X}} \right)}}} & {{Equation}\mspace{14mu} 34}\end{matrix}$Step B•3 (counting the number of iterations and estimating a codeword):increment l_(mimo) if l_(mimo)<l_(mimo,max) and return to step B•2.Assuming that l_(mimo)=l_(mimo,max), the estimated codeword is sought asin the following Equation.

$\begin{matrix}{{Math}\mspace{14mu} 35} & \; \\{{\hat{u}}_{n_{X}} = \left\{ \begin{matrix}1 & {L_{l_{mimo},n_{X}} \geq 0} \\{- 1} & {L_{l_{mimo},n_{X}} < 0}\end{matrix} \right.} & {{Equation}\mspace{14mu} 35}\end{matrix}$

Here, let X=a, b.

FIG. 3 is an example of the structure of a transmission device 300 inthe present embodiment. An encoder 302A receives information (data) 301Aand a frame structure signal 313 as inputs and, in accordance with theframe structure signal 313, performs error correction coding such asconvolutional coding, LDPC coding, turbo coding, or the like, outputtingencoded data 303A. (The frame structure signal 313 includes informationsuch as the error correction method used for error correction coding ofdata, the encoding ratio, the block length, and the like. The encoder302A uses the error correction method indicated by the frame structuresignal 313. Furthermore, the error correction method may be switched.)

An interleaver 304A receives the encoded data 303A and the framestructure signal 313 as inputs and performs interleaving, i.e. changingthe order of the data, to output interleaved data 305A. (The method ofinterleaving may be switched based on the frame structure signal 313.)

A mapper 306A receives the interleaved data 305A and the frame structuresignal 313 as inputs, performs modulation such as Quadrature Phase ShiftKeying (QPSK), 16 Quadrature Amplitude Modulation (16QAM), 64 QuadratureAmplitude Modulation (64QAM), or the like, and outputs a resultingbaseband signal 307A. (The method of modulation may be switched based onthe frame structure signal 313.)

FIGS. 24A and 24B are an example of a mapping method over an IQ plane,having an in-phase component I and a quadrature component Q, to form abaseband signal in QPSK modulation. For example, as shown in FIG. 24A,if the input data is “00”, the output is I=1.0, Q=1.0. Similarly, forinput data of “01”, the output is I=—1.0, Q=1.0, and so forth. FIG. 24Bis an example of a different method of mapping in an IQ plane for QPSKmodulation than FIG. 24A. The difference between FIG. 24B and FIG. 24Ais that the signal points in FIG. 24A have been rotated around theorigin to yield the signal points of FIG. 24B. Non-Patent Literature 9and Non-Patent Literature 10 describe such a constellation rotationmethod, and the Cyclic Q Delay described in Non-Patent Literature 9 andNon-Patent Literature 10 may also be adopted. As another example apartfrom FIGS. 24A and 24B, FIGS. 25A and 25B show signal point layout inthe IQ plane for 16QAM. The example corresponding to FIG. 24A is shownin FIG. 25A, and the example corresponding to FIG. 24B is shown in FIG.25B.

An encoder 302B receives information (data) 301B and the frame structuresignal 313 as inputs and, in accordance with the frame structure signal313, performs error correction coding such as convolutional coding, LDPCcoding, turbo coding, or the like, outputting encoded data 303B. (Theframe structure signal 313 includes information such as the errorcorrection method used, the encoding ratio, the block length, and thelike. The error correction method indicated by the frame structuresignal 313 is used. Furthermore, the error correction method may beswitched.)

An interleaver 304B receives the encoded data 303B and the framestructure signal 313 as inputs and performs interleaving, i.e. changingthe order of the data, to output interleaved data 305B. (The method ofinterleaving may be switched based on the frame structure signal 313.)

A mapper 306B receives the interleaved data 305B and the frame structuresignal 313 as inputs, performs modulation such as Quadrature Phase ShiftKeying (QPSK), 16 Quadrature Amplitude Modulation (16QAM), 64 QuadratureAmplitude Modulation (64QAM), or the like, and outputs a resultingbaseband signal 307B. (The method of modulation may be switched based onthe frame structure signal 313.)

A weighting information generating unit 314 receives the frame structuresignal 313 as an input and outputs information 315 regarding a weightingmethod based on the frame structure signal 313. The weighting method ischaracterized by regular hopping between weights.

A weighting unit 308A receives the baseband signal 307A, the basebandsignal 307B, and the information 315 regarding the weighting method, andbased on the information 315 regarding the weighting method, performsweighting on the baseband signal 307A and the baseband signal 307B andoutputs a signal 309A resulting from the weighting. Details on theweighting method are provided later.

A wireless unit 310A receives the signal 309A resulting from theweighting as an input and performs processing such as orthogonalmodulation, band limiting, frequency conversion, amplification, and thelike, outputting a transmission signal 311A. A transmission signal 511Ais output as a radio wave from an antenna 312A.

A weighting unit 308B receives the baseband signal 307A, the basebandsignal 307B, and the information 315 regarding the weighting method, andbased on the information 315 regarding the weighting method, performsweighting on the baseband signal 307A and the baseband signal 307B andoutputs a signal 309B resulting from the weighting.

FIG. 26 shows the structure of a weighting unit. The baseband signal307A is multiplied by w11(t), yielding w11(t)s1(t), and is multiplied byw21(t), yielding w21(t)s1(t). Similarly, the baseband signal 307B ismultiplied by w12(t) to generate w12(t)s2(t) and is multiplied by w22(t)to generate w22(t)s2(t). Next, z1(t)=w11(t)s1(t)+w12(t)s2(t) andz2(t)=w21(t)s1(t)+w22(t)s2(t) are obtained.

Details on the weighting method are provided later.

A wireless unit 310B receives the signal 309B resulting from theweighting as an input and performs processing such as orthogonalmodulation, band limiting, frequency conversion, amplification, and thelike, outputting a transmission signal 311B. A transmission signal 511Bis output as a radio wave from an antenna 312B.

FIG. 4 shows an example of the structure of a transmission device 400that differs from FIG. 3. The differences in FIG. 4 from FIG. 3 aredescribed.

An encoder 402 receives information (data) 401 and the frame structuresignal 313 as inputs and, in accordance with the frame structure signal313, performs error correction coding and outputs encoded data 402.

A distribution unit 404 receives the encoded data 403 as an input,distributes the data 403, and outputs data 405A and data 405B. Note thatin FIG. 4, one encoder is shown, but the number of encoders is notlimited in this way. The present invention may similarly be embodiedwhen the number of encoders is m (where m is an integer greater than orequal to one) and the distribution unit divides encoded data generatedby each encoder into two parts and outputs the divided data.

FIG. 5 shows an example of a frame structure in the time domain for atransmission device according to the present embodiment. A symbol 500_1is a symbol for notifying the reception device of the transmissionmethod. For example, the symbol 500_1 conveys information such as theerror correction method used for transmitting data symbols, the encodingratio, and the modulation method used for transmitting data symbols.

The symbol 501_1 is for estimating channel fluctuation for the modulatedsignal z1(t) (where t is time) transmitted by the transmission device.The symbol 502_1 is the data symbol transmitted as symbol number u (inthe time domain) by the modulated signal z1(t), and the symbol 503_1 isthe data symbol transmitted as symbol number u+1 by the modulated signalz1(t).

The symbol 501_2 is for estimating channel fluctuation for the modulatedsignal z2(t) (where t is time) transmitted by the transmission device.The symbol 502_2 is the data symbol transmitted as symbol number u bythe modulated signal z2(t), and the symbol 503_2 is the data symboltransmitted as symbol number u+1 by the modulated signal z2(t).

The following describes the relationships between the modulated signalsz1(t) and z2(t) transmitted by the transmission device and the receivedsignals r1(t) and r2(t) received by the reception device.

In FIGS. 5, 504#1 and 504#2 indicate transmit antennas in thetransmission device, and 505#1 and 505#2 indicate receive antennas inthe reception device. The transmission device transmits the modulatedsignal z1(t) from transmit antenna 504#1 and transmits the modulatedsignal z2(t) from transmit antenna 504#2. In this case, the modulatedsignal z1(t) and the modulated signal z2(t) are assumed to occupy thesame (a shared/common) frequency (bandwidth). Letting the channelfluctuation for the transmit antennas of the transmission device and theantennas of the reception device be h₁₁(t), h₁₂(t), h₂₁(t), and h₂₂(t),the signal received by the receive antenna 505#1 of the reception devicebe r1(t), and the signal received by the receive antenna 505#2 of thereception device be r2(t), the following relationship holds.

$\begin{matrix}{{Math}\mspace{14mu} 36} & \; \\{\begin{pmatrix}{r\; 1\;(t)} \\{r\; 2\;(t)}\end{pmatrix} = {\begin{pmatrix}{h_{11}(t)} & {h_{12}(t)} \\{h_{21}(t)} & {h_{22}(t)}\end{pmatrix}\begin{pmatrix}{z\; 1\;(t)} \\{z\; 2\;(t)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 36}\end{matrix}$

FIG. 6 relates to the weighting method (precoding method) in the presentembodiment. A weighting unit 600 integrates the weighting units 308A and308B in FIG. 3. As shown in FIG. 6, a stream s1(t) and a stream s2(t)correspond to the baseband signals 307A and 307B in FIG. 3. In otherwords, the streams s1(t) and s2(t) are the baseband signal in-phasecomponents I and quadrature components Q when mapped according to amodulation scheme such as QPSK, 16QAM, 64QAM, or the like. As indicatedby the frame structure of FIG. 6, the stream s1(t) is represented ass1(u) at symbol number u, as s1(u+1) at symbol number u+1, and so forth.Similarly, the stream s2(t) is represented as s2(u) at symbol number u,as s2(u+1) at symbol number u+1, and so forth. The weighting unit 600receives the baseband signals 307A (s1(t)) and 307B (s2(t)) and theinformation 315 regarding weighting information in FIG. 3 as inputs,performs weighting in accordance with the information 315 regardingweighting, and outputs the signals 309A (z1(t)) and 309B (z2(t)) afterweighting in FIG. 3. In this case, z1(t) and z2(t) are represented asfollows.

For symbol number 4i (where i is an integer greater than or equal tozero):

$\begin{matrix}{{Math}\mspace{14mu} 37} & \; \\{\begin{pmatrix}{z\; 1\;\left( {4\; i} \right)} \\{z\; 2\;\left( {4\; i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{{j\frac{3}{4}\pi}\;}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {4\; i} \right)} \\{s\; 2\;\left( {4\; i} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 37}\end{matrix}$Here, j is an imaginary unit.For symbol number 4i+1:

$\begin{matrix}{{Math}\mspace{14mu} 38} & \; \\{\begin{pmatrix}{z\; 1\;\left( {{4\; i} + 1} \right)} \\{z\; 2\;\left( {{4\; i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{{j\frac{3}{4}\pi}\;} & {\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {{4\; i} + 1} \right)} \\{s\; 2\;\left( {{4\; i} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 38}\end{matrix}$For symbol number 4i+2:

$\begin{matrix}{{Math}\mspace{14mu} 39} & \; \\{\begin{pmatrix}{z\; 1\;\left( {{4\; i} + 2} \right)} \\{z\; 2\;\left( {{4\; i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{{j\frac{3}{4}\pi}\;} \\{\mathbb{e}}^{{j\; 0}\;} & {\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {{4\; i} + 2} \right)} \\{s\; 2\;\left( {{4\; i} + 2} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 39}\end{matrix}$For symbol number 4i+3:

$\begin{matrix}{{Math}\mspace{14mu} 40} & \; \\{\begin{pmatrix}{z\; 1\;\left( {{4\; i} + 3} \right)} \\{z\; 2\;\left( {{4\; i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\frac{3}{4}\pi}\;} & {\mathbb{e}}^{{j\; 0}\;} \\{\mathbb{e}}^{{j\; 0}\;} & {\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {{4\; i} + 3} \right)} \\{s\; 2\;\left( {{4\; i} + 3} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 40}\end{matrix}$

In this way, the weighting unit in FIG. 6 regularly hops betweenprecoding weights over a four-slot period (cycle). (While precodingweights have been described as being hopped between regularly over fourslots, the number of slots for regular hopping is not limited to four.)

Incidentally, Non-Patent Literature 4 describes switching the precodingweights for each slot. This switching of precoding weights ischaracterized by being random. On the other hand, in the presentembodiment, a certain period (cycle) is provided, and the precodingweights are hopped between regularly. Furthermore, in each 2×2 precodingweight matrix composed of four precoding weights, the absolute value ofeach of the four precoding weights is equivalent to (1/sqrt(2)), andhopping is regularly performed between precoding weight matrices havingthis characteristic.

In an LOS environment, if a special precoding matrix is used, receptionquality may greatly improve, yet the special precoding matrix differsdepending on the conditions of direct waves. In an LOS environment,however, a certain tendency exists, and if precoding matrices are hoppedbetween regularly in accordance with this tendency, the receptionquality of data greatly improves. On the other hand, when precodingmatrices are hopped between at random, a precoding matrix other than theabove-described special precoding matrix may exist, and the possibilityof performing precoding only with biased precoding matrices that are notsuitable for the LOS environment also exists. Therefore, in an LOSenvironment, excellent reception quality may not always be obtained.Accordingly, there is a need for a precoding hopping method suitable foran LOS environment. The present invention proposes such a precodingmethod.

FIG. 7 is an example of the structure of a reception device 700 in thepresent embodiment. A wireless unit 703_X receives, as an input, areceived signal 702_X received by an antenna 701_X, performs processingsuch as frequency conversion, quadrature demodulation, and the like, andoutputs a baseband signal 704_X. A channel fluctuation estimating unit705_1 for the modulated signal z1 transmitted by the transmission devicereceives the baseband signal 704_X as an input, extracts a referencesymbol 501_1 for channel estimation as in FIG. 5, estimates a valuecorresponding to h₁₁ in Equation 36, and outputs a channel estimationsignal 706_1.

A channel fluctuation estimating unit 705_2 for the modulated signal z2transmitted by the transmission device receives the baseband signal704_X as an input, extracts a reference symbol 501_2 for channelestimation as in FIG. 5, estimates a value corresponding to h₁₂ inEquation 36, and outputs a channel estimation signal 706_2.

A wireless unit 703_Y receives, as input, a received signal 702_Yreceived by an antenna 701_Y, performs processing such as frequencyconversion, quadrature demodulation, and the like, and outputs abaseband signal 704_Y.

A channel fluctuation estimating unit 707_1 for the modulated signal z1transmitted by the transmission device receives the baseband signal704_Y as an input, extracts a reference symbol 501_1 for channelestimation as in FIG. 5, estimates a value corresponding to h₂₁ inEquation 36, and outputs a channel estimation signal 708_1.

A channel fluctuation estimating unit 707_2 for the modulated signal z2transmitted by the transmission device receives the baseband signal704_Y as an input, extracts a reference symbol 501_2 for channelestimation as in FIG. 5, estimates a value corresponding to h₂₂ inEquation 36, and outputs a channel estimation signal 708_2.

A control information decoding unit 709 receives the baseband signal704_X and the baseband signal 704_Y as inputs, detects the symbol 500_1that indicates the transmission method as in FIG. 5, and outputs asignal 710 regarding information on the transmission method indicated bythe transmission device.

A signal processing unit 711 receives, as inputs, the baseband signals704_X and 704_Y, the channel estimation signals 706_1, 706_2, 708_1, and708_2, and the signal 710 regarding information on the transmissionmethod indicated by the transmission device, performs detection anddecoding, and outputs received data 712_1 and 712_2.

Next, operations by the signal processing unit 711 in FIG. 7 aredescribed in detail. FIG. 8 is an example of the structure of the signalprocessing unit 711 in the present embodiment. FIG. 8 shows an INNERMIMO detector, a soft-in/soft-out decoder, and a weighting coefficientgenerating unit as the main elements. Non-Patent Literature 2 andNon-Patent Literature 3 describe the method of iterative decoding withthis structure. The MIMO system described in Non-Patent Literature 2 andNon-Patent Literature 3 is a spatial multiplexing MIMO system, whereasthe present embodiment differs from Non-Patent Literature 2 andNon-Patent Literature 3 by describing a MIMO system that changesprecoding weights with time. Letting the (channel) matrix in Equation 36be H(t), the precoding weight matrix in FIG. 6 be W(t) (where theprecoding weight matrix changes over t), the received vector beR(t)=(r1(t),r2(t))^(T), and the stream vector be S(t)=(s1(t),s2(t))^(T),the following Equation holds.Math 41R(t)=H(t)W(t)S(t)  Equation 41

In this case, the reception device can apply the decoding method inNon-Patent Literature 2 and Non-Patent Literature 3 to the receivedvector R(t) by considering H(t)W(t) as the channel matrix.

Therefore, a weighting coefficient generating unit 819 in FIG. 8receives, as input, a signal 818 regarding information on thetransmission method indicated by the transmission device (correspondingto 710 in FIG. 7) and outputs a signal 820 regarding information onweighting coefficients.

An INNER MIMO detector 803 receives the signal 820 regarding informationon weighting coefficients as input and, using the signal 820, performsthe calculation in Equation 41. Iterative detection and decoding is thusperformed. The following describes operations thereof.

In the signal processing unit in FIG. 8, a processing method such asthat shown in FIG. 10 is necessary for iterative decoding (iterativedetection). First, one codeword (or one frame) of the modulated signal(stream) s1 and one codeword (or one frame) of the modulated signal(stream) s2 are decoded. As a result, the Log-Likelihood Ratio (LLR) ofeach bit of the one codeword (or one frame) of the modulated signal(stream) s1 and of the one codeword (or one frame) of the modulatedsignal (stream) s2 is obtained from the soft-in/soft-out decoder.Detection and decoding is performed again using the LLR. Theseoperations are performed multiple times (these operations being referredto as iterative decoding (iterative detection)). Hereinafter,description focuses on the method of generating the log-likelihood ratio(LLR) of a symbol at a particular time in one frame.

In FIG. 8, a storage unit 815 receives, as inputs, a baseband signal801X (corresponding to the baseband signal 704_X in FIG. 7), a channelestimation signal group 802X (corresponding to the channel estimationsignals 706_1 and 706_2 in FIG. 7), a baseband signal 801Y(corresponding to the baseband signal 704_Y in FIG. 7), and a channelestimation signal group 802Y (corresponding to the channel estimationsignals 708_1 and 708_2 in FIG. 7). In order to achieve iterativedecoding (iterative detection), the storage unit 815 calculates H(t)W(t)in Equation 41 and stores the calculated matrix as a transformed channelsignal group. The storage unit 815 outputs the above signals whennecessary as a baseband signal 816X, a transformed channel estimationsignal group 817X, a baseband signal 816Y, and a transformed channelestimation signal group 817Y.

Subsequent operations are described separately for initial detection andfor iterative decoding (iterative detection).

<Initial Detection>

The INNER MIMO detector 803 receives, as inputs, the baseband signal801X, the channel estimation signal group 802X, the baseband signal801Y, and the channel estimation signal group 802Y. Here, the modulationmethod for the modulated signal (stream) s1 and the modulated signal(stream) s2 is described as 16QAM.

The INNER MIMO detector 803 first calculates H(t)W(t) from the channelestimation signal group 802X and the channel estimation signal group802Y to seek candidate signal points corresponding to the basebandsignal 801X. FIG. 11 shows such calculation. In FIG. 11, each black dot(●) is a candidate signal point in the IQ plane. Since the modulationmethod is 16QAM, there are 256 candidate signal points. (Since FIG. 11is only for illustration, not all 256 candidate signal points areshown.) Here, letting the four bits transferred by modulated signal s1be b0, b1, b2, and b3, and the four bits transferred by modulated signals2 be b4, b5, b6, and b7, candidate signal points corresponding to (b0,b1, b2, b3, b4, b5, b6, b7) in FIG. 11 exist. The squared Euclidiandistance is sought between a received signal point 1101 (correspondingto the baseband signal 801X) and each candidate signal point. Eachsquared Euclidian distance is divided by the noise variance σ².Accordingly, E_(X)(b0, b1, b2, b3, b4, b5, b6, b7), i.e. the value ofthe squared Euclidian distance between a candidate signal pointcorresponding to (b0, b1, b2, b3, b4, b5, b6, b7) and a received signalpoint, divided by the noise variance, is sought. Note that the basebandsignals and the modulated signals s1 and s2 are each complex signals.

Similarly, H(t)W(t) is calculated from the channel estimation signalgroup 802X and the channel estimation signal group 802Y, candidatesignal points corresponding to the baseband signal 801Y are sought, thesquared Euclidian distance for the received signal point (correspondingto the baseband signal 801Y) is sought, and the squared Euclidiandistance is divided by the noise variance σ². Accordingly, E_(Y)(b0, b1,b2, b3, b4, b5, b6, b7), i.e. the value of the squared Euclidiandistance between a candidate signal point corresponding to (b0, b1, b2,b3, b4, b5, b6, b7) and a received signal point, divided by the noisevariance, is sought.

Then E_(X)(b0, b1, b2, b3, b4, b5, b6, b7)+E_(Y)(b0, b1, b2, b3, b4, b5,b6, b7)=E(b0, b1, b2, b3, b4, b5, b6, b7) is sought.

The INNER MIMO detector 803 outputs E(b0, b1, b2, b3, b4, b5, b6, b7) asa signal 804.

A log-likelihood calculating unit 805A receives the signal 804 as input,calculates the log likelihood for bits b0, b1, b2, and b3, and outputs alog-likelihood signal 806A. Note that during calculation of the loglikelihood, the log likelihood for “1” and the log likelihood for “0”are calculated. The calculation method is as shown in Equations 28, 29,and 30. Details can be found in Non-Patent Literature 2 and Non-PatentLiterature 3.

Similarly, a log-likelihood calculating unit 805B receives the signal804 as input, calculates the log likelihood for bits b4, b5, b6, and b7,and outputs a log-likelihood signal 806B.

A deinterleaver (807A) receives the log-likelihood signal 806A as aninput, performs deinterleaving corresponding to the interleaver (theinterleaver (304A) in FIG. 3), and outputs a deinterleavedlog-likelihood signal 808A.

Similarly, a deinterleaver (807B) receives the log-likelihood signal806B as an input, performs deinterleaving corresponding to theinterleaver (the interleaver (304B) in FIG. 3), and outputs adeinterleaved log-likelihood signal 808B.

A log-likelihood ratio calculating unit 809A receives the interleavedlog-likelihood signal 808A as an input, calculates the log-likelihoodratio (LLR) of the bits encoded by the encoder 302A in FIG. 3, andoutputs a log-likelihood ratio signal 810A.

Similarly, a log-likelihood ratio calculating unit 809B receives theinterleaved log-likelihood signal 808B as an input, calculates thelog-likelihood ratio (LLR) of the bits encoded by the encoder 302B inFIG. 3, and outputs a log-likelihood ratio signal 810B.

A soft-in/soft-out decoder 811A receives the log-likelihood ratio signal810A as an input, performs decoding, and outputs a decodedlog-likelihood ratio 812A.

Similarly, a soft-in/soft-out decoder 811B receives the log-likelihoodratio signal 810B as an input, performs decoding, and outputs a decodedlog-likelihood ratio 812B.

<Iterative Decoding (Iterative Detection), Number of Iterations k>

An interleaver (813A) receives the log-likelihood ratio 812A decoded bythe soft-in/soft-out decoder in the (k−1)^(th) iteration as an input,performs interleaving, and outputs an interleaved log-likelihood ratio814A. The interleaving pattern in the interleaver (813A) is similar tothe interleaving pattern in the interleaver (304A) in FIG. 3.

An interleaver (813B) receives the log-likelihood ratio 812B decoded bythe soft-in/soft-out decoder in the (k−1)^(th) iteration as an input,performs interleaving, and outputs an interleaved log-likelihood ratio814B. The interleaving pattern in the interleaver (813B) is similar tothe interleaving pattern in the interleaver (304B) in FIG. 3.

The INNER MIMO detector 803 receives, as inputs, the baseband signal816X, the transformed channel estimation signal group 817X, the basebandsignal 816Y, the transformed channel estimation signal group 817Y, theinterleaved log-likelihood ratio 814A, and the interleavedlog-likelihood ratio 814B. The reason for using the baseband signal816X, the transformed channel estimation signal group 817X, the basebandsignal 816Y, and the transformed channel estimation signal group 817Yinstead of the baseband signal 801X, the channel estimation signal group802X, the baseband signal 801Y, and the channel estimation signal group802Y is because a delay occurs due to iterative decoding.

The difference between operations by the INNER MIMO detector 803 foriterative decoding and for initial detection is the use of theinterleaved log-likelihood ratio 814A and the interleaved log-likelihoodratio 814B during signal processing. The INNER MIMO detector 803 firstseeks E(b0, b1, b2, b3, b4, b5, b6, b7), as during initial detection.Additionally, coefficients corresponding to Equations 11 and 32 aresought from the interleaved log-likelihood ratio 814A and theinterleaved log-likelihood ratio 914B. The value E(b0, b1, b2, b3, b4,b5, b6, b7) is adjusted using the sought coefficients, and the resultingvalue E′(b0, b1, b2, b3, b4, b5, b6, b7) is output as the signal 804.

The log-likelihood calculating unit 805A receives the signal 804 asinput, calculates the log likelihood for bits b0, b1, b2, and b3, andoutputs the log-likelihood signal 806A. Note that during calculation ofthe log likelihood, the log likelihood for “1” and the log likelihoodfor “0” are calculated. The calculation method is as shown in Equations31, 32, 33, 34, and 35. Details can be found in Non-Patent Literature 2and Non-Patent Literature 3.

Similarly, the log-likelihood calculating unit 805B receives the signal804 as input, calculates the log likelihood for bits b4, b5, b6, and b7,and outputs the log-likelihood signal 806B. Operations by thedeinterleaver onwards are similar to initial detection.

Note that while FIG. 8 shows the structure of the signal processing unitwhen performing iterative detection, iterative detection is not alwaysessential for obtaining excellent reception quality, and a structure notincluding the interleavers 813A and 813B, which are necessary only foriterative detection, is possible. In such a case, the INNER MIMOdetector 803 does not perform iterative detection.

The main part of the present embodiment is calculation of H(t)W(t). Notethat as shown in Non-Patent Literature 5 and the like, QR decompositionmay be used to perform initial detection and iterative detection.

Furthermore, as shown in Non-Patent Literature 11, based on H(t)W(t),linear operation of the Minimum Mean Squared Error (MMSE) and ZeroForcing (ZF) may be performed in order to perform initial detection.

FIG. 9 is the structure of a different signal processing unit than FIG.8 and is for the modulated signal transmitted by the transmission devicein FIG. 4. The difference with FIG. 8 is the number of soft-in/soft-outdecoders. A soft-in/soft-out decoder 901 receives, as inputs, thelog-likelihood ratio signals 810A and 810B, performs decoding, andoutputs a decoded log-likelihood ratio 902. A distribution unit 903receives the decoded log-likelihood ratio 902 as an input anddistributes the log-likelihood ratio 902. Other operations are similarto FIG. 8.

FIGS. 12A and 12B show BER characteristics for a transmission methodusing the precoding weights of the present embodiment under similarconditions to FIGS. 29A and 29B. FIG. 12A shows the BER characteristicsof Max-log A Posteriori Probability (APP) without iterative detection(see Non-Patent Literature 1 and Non-Patent Literature 2), and FIG. 12Bshows the BER characteristics of Max-log-APP with iterative detection(see Non-Patent Literature 1 and Non-Patent Literature 2) (number ofiterations: five). Comparing FIGS. 12A, 12B, 29A, and 29B shows how ifthe transmission method of the present embodiment is used, the BERcharacteristics when the Rician factor is large greatly improve over theBER characteristics when using spatial multiplexing MIMO, therebyconfirming the usefulness of the method in the present embodiment.

As described above, when a transmission device transmits a plurality ofmodulated signals from a plurality of antennas in a MIMO system, theadvantageous effect of improved transmission quality, as compared toconventional spatial multiplexing MIMO, is achieved in an LOSenvironment in which direct waves dominate by hopping between precodingweights regularly over time, as in the present embodiment.

In the present embodiment, and in particular with regards to thestructure of the reception device, operations have been described for alimited number of antennas, but the present invention may be embodied inthe same way even if the number of antennas increases. In other words,the number of antennas in the reception device does not affect theoperations or advantageous effects of the present embodiment.Furthermore, in the present embodiment, the example of LDPC coding hasparticularly been explained, but the present invention is not limited toLDPC coding. Furthermore, with regards to the decoding method, thesoft-in/soft-out decoders are not limited to the example of sum-productdecoding. Another soft-in/soft-out decoding method may be used, such asa BCJR algorithm, a SOYA algorithm, a Max-log-MAP algorithm, and thelike. Details are provided in Non-Patent Literature 6.

Additionally, in the present embodiment, the example of a single carriermethod has been described, but the present invention is not limited inthis way and may be similarly embodied for multi-carrier transmission.Accordingly, when using a method such as spread spectrum communication,Orthogonal Frequency-Division Multiplexing (OFDM), Single CarrierFrequency Division Multiple Access (SC-FDMA), Single Carrier OrthogonalFrequency-Division Multiplexing (SC-OFDM), or wavelet OFDM as describedin Non-Patent Literature 7 and the like, for example, the presentinvention may be similarly embodied. Furthermore, in the presentembodiment, symbols other than data symbols, such as pilot symbols(preamble, unique word, and the like), symbols for transmission ofcontrol information, and the like, may be arranged in the frame in anyway.

The following describes an example of using OFDM as an example of amulti-carrier method.

FIG. 13 shows the structure of a transmission device when using OFDM. InFIG. 13, elements that operate in a similar way to FIG. 3 bear the samereference signs.

An OFDM related processor 1301A receives, as input, the weighted signal309A, performs processing related to OFDM, and outputs a transmissionsignal 1302A. Similarly, an OFDM related processor 1301B receives, asinput, the weighted signal 309B, performs processing related to OFDM,and outputs a transmission signal 1302B.

FIG. 14 shows an example of a structure from the OFDM related processors1301A and 1301B in FIG. 13 onwards. The part from 1401A to 1410A isrelated to the part from 1301A to 312A in FIG. 13, and the part from1401B to 1410B is related to the part from 1301B to 312B in FIG. 13.

A serial/parallel converter 1402A performs serial/parallel conversion ona weighted signal 1401A (corresponding to the weighted signal 309A inFIG. 13) and outputs a parallel signal 1403A.

A reordering unit 1404A receives a parallel signal 1403A as input,performs reordering, and outputs a reordered signal 1405A. Reordering isdescribed in detail later.

An inverse fast Fourier transformer 1406A receives the reordered signal1405A as an input, performs a fast Fourier transform, and outputs a fastFourier transformed signal 1407A.

A wireless unit 1408A receives the fast Fourier transformed signal 1407Aas an input, performs processing such as frequency conversion,amplification, and the like, and outputs a modulated signal 1409A. Themodulated signal 1409A is output as a radio wave from an antenna 1410A.

A serial/parallel converter 1402B performs serial/parallel conversion ona weighted signal 1401B (corresponding to the weighted signal 309B inFIG. 13) and outputs a parallel signal 1403B.

A reordering unit 1404B receives a parallel signal 1403B as input,performs reordering, and outputs a reordered signal 1405B. Reordering isdescribed in detail later.

An inverse fast Fourier transformer 1406B receives the reordered signal1405B as an input, performs a fast Fourier transform, and outputs a fastFourier transformed signal 1407B.

A wireless unit 1408B receives the fast Fourier transformed signal 1407Bas an input, performs processing such as frequency conversion,amplification, and the like, and outputs a modulated signal 1409B. Themodulated signal 1409B is output as a radio wave from an antenna 1410B.

In the transmission device of FIG. 3, since the transmission method doesnot use multi-carrier, precoding hops to form a four-slot period(cycle), as shown in FIG. 6, and the precoded symbols are arranged inthe time domain. When using a multi-carrier transmission method as inthe OFDM method shown in FIG. 13, it is of course possible to arrangethe precoded symbols in the time domain as in FIG. 3 for each(sub)carrier. In the case of a multi-carrier transmission method,however, it is possible to arrange symbols in the frequency domain, orin both the frequency and time domains. The following describes thesearrangements.

FIGS. 15A and 15B show an example of a method of reordering symbols byreordering units 1401A and 1401B in FIG. 14, the horizontal axisrepresenting frequency, and the vertical axis representing time. Thefrequency domain runs from (sub)carrier 0 through (sub)carrier 9. Themodulated signals z1 and z2 use the same frequency bandwidth at the sametime. FIG. 15A shows the reordering method for symbols of the modulatedsignal z1, and FIG. 15B shows the reordering method for symbols of themodulated signal z2. Numbers #1, #2, #3, #4, . . . are assigned to inorder to the symbols of the weighted signal 1401A which is input intothe serial/parallel converter 1402A. At this point, symbols are assignedregularly, as shown in FIG. 15A. The symbols #1, #2, #3, #4, . . . arearranged in order starting from carrier 0. The symbols #1 through #9 areassigned to time $1, and subsequently, the symbols #10 through #19 areassigned to time $2.

Similarly, numbers #1, #2, #3, #4, . . . are assigned in order to thesymbols of the weighted signal 1401B which is input into theserial/parallel converter 1402B. At this point, symbols are assignedregularly, as shown in FIG. 15B. The symbols #1, #2, #3, #4, . . . arearranged in order starting from carrier 0. The symbols #1 through #9 areassigned to time $1, and subsequently, the symbols #10 through #19 areassigned to time $2. Note that the modulated signals z1 and z2 arecomplex signals.

The symbol group 1501 and the symbol group 1502 shown in FIGS. 15A and15B are the symbols for one period (cycle) when using the precodingweight hopping method shown in FIG. 6. Symbol #0 is the symbol whenusing the precoding weight of slot 4i in FIG. 6. Symbol #1 is the symbolwhen using the precoding weight of slot 4i+1 in FIG. 6. Symbol #2 is thesymbol when using the precoding weight of slot 4i+2 in FIG. 6. Symbol #3is the symbol when using the precoding weight of slot 4i+3 in FIG. 6.Accordingly, symbol #x is as follows. When x mod 4 is 0, the symbol #xis the symbol when using the precoding weight of slot 4i in FIG. 6. Whenx mod 4 is 1, the symbol #x is the symbol when using the precodingweight of slot 4i+1 in FIG. 6. When x mod 4 is 2, the symbol #x is thesymbol when using the precoding weight of slot 4i+2 in FIG. 6. When xmod 4 is 3, the symbol #x is the symbol when using the precoding weightof slot 4i+3 in FIG. 6.

In this way, when using a multi-carrier transmission method such asOFDM, unlike during single carrier transmission, symbols can be arrangedin the frequency domain. Furthermore, the ordering of symbols is notlimited to the ordering shown in FIGS. 15A and 15B. Other examples aredescribed with reference to FIGS. 16A, 16B, 17A, and 17B.

FIGS. 16A and 16B show an example of a method of reordering symbols bythe reordering units 1404A and 1404B in FIG. 14, the horizontal axisrepresenting frequency, and the vertical axis representing time, thatdiffers from FIGS. 15A and 15B. FIG. 16A shows the reordering method forsymbols of the modulated signal z1, and FIG. 16B shows the reorderingmethod for symbols of the modulated signal z2. The difference in FIGS.16A and 16B as compared to FIGS. 15A and 15B is that the reorderingmethod of the symbols of the modulated signal z1 differs from thereordering method of the symbols of the modulated signal z2. In FIG.16B, symbols #0 through #5 are assigned to carriers 4 through 9, andsymbols #6 through #9 are assigned to carriers 0 through 3.Subsequently, symbols #10 through #19 are assigned regularly in the sameway. At this point, as in FIGS. 15A and 15B, the symbol group 1601 andthe symbol group 1602 shown in FIGS. 16A and 16B are the symbols for oneperiod (cycle) when using the precoding weight hopping method shown inFIG. 6.

FIGS. 17A and 17B show an example of a method of reordering symbols bythe reordering units 1404A and 1404B in FIG. 14, the horizontal axisrepresenting frequency, and the vertical axis representing time, thatdiffers from FIGS. 15A and 15B. FIG. 17A shows the reordering method forsymbols of the modulated signal z1, and FIG. 17B shows the reorderingmethod for symbols of the modulated signal z2. The difference in FIGS.17A and 17B as compared to FIGS. 15A and 15B is that whereas the symbolsare arranged in order by carrier in FIGS. 15A and 15B, the symbols arenot arranged in order by carrier in FIGS. 17A and 17B. It is obviousthat, in FIGS. 17A and 17B, the reordering method of the symbols of themodulated signal z1 may differ from the reordering method of the symbolsof the modulated signal z2, as in FIGS. 16A and 16B.

FIGS. 18A and 18B show an example of a method of reordering symbols bythe reordering units 1404A and 1404B in FIG. 14, the horizontal axisrepresenting frequency, and the vertical axis representing time, thatdiffers from FIGS. 15A through 17B. FIG. 18A shows the reordering methodfor symbols of the modulated signal z1, and FIG. 18B shows thereordering method for symbols of the modulated signal z2. In FIGS. 15Athrough 17B, symbols are arranged in the frequency domain, whereas inFIGS. 18A and 18B, symbols are arranged in both the frequency and timedomains.

In FIG. 6, an example has been described of hopping between precodingweights over four slots. Here, however, an example of hopping over eightslots is described. The symbol groups 1801 and 1802 shown in FIGS. 18Aand 18B are the symbols for one period (cycle) when using the precodingweight hopping method (and are therefore eight-symbol groups). Symbol #0is the symbol when using the precoding weight of slot 8i. Symbol #1 isthe symbol when using the precoding weight of slot 8i+1. Symbol #2 isthe symbol when using the precoding weight of slot 8i+2. Symbol #3 isthe symbol when using the precoding weight of slot 8i+3. Symbol #4 isthe symbol when using the precoding weight of slot 8i+4. Symbol #5 isthe symbol when using the precoding weight of slot 8i+5. Symbol #6 isthe symbol when using the precoding weight of slot 8i+6. Symbol #7 isthe symbol when using the precoding weight of slot 8i+7. Accordingly,symbol #x is as follows. When x mod 8 is 0, the symbol #x is the symbolwhen using the precoding weight of slot 8i. When x mod 8 is 1, thesymbol #x is the symbol when using the precoding weight of slot 8i+1.When x mod 8 is 2, the symbol #x is the symbol when using the precodingweight of slot 8i+2. When x mod 8 is 3, the symbol #x is the symbol whenusing the precoding weight of slot 8i+3. When x mod 8 is 4, the symbol#x is the symbol when using the precoding weight of slot 8i+4. When xmod 8 is 5, the symbol #x is the symbol when using the precoding weightof slot 8i+5. When x mod 8 is 6, the symbol #x is the symbol when usingthe precoding weight of slot 8i+6. When x mod 8 is 7, the symbol #x isthe symbol when using the precoding weight of slot 8i+7. In the symbolordering in FIGS. 18A and 18B, four slots in the time domain and twoslots in the frequency domain for a total of 4×2=8 slots are used toarrange symbols for one period (cycle). In this case, letting the numberof symbols in one period (cycle) be m×n symbols (in other words, m×nprecoding weights exist), the number of slots (the number of carriers)in the frequency domain used to arrange symbols in one period (cycle) ben, and the number of slots used in the time domain be m, m should begreater than n. This is because the phase of direct waves fluctuatesmore slowly in the time domain than in the frequency domain. Therefore,since the precoding weights are changed in the present embodiment tominimize the influence of steady direct waves, it is preferable toreduce the fluctuation in direct waves in the period (cycle) forchanging the precoding weights. Accordingly, m should be greater than n.Furthermore, considering the above points, rather than reorderingsymbols only in the frequency domain or only in the time domain, directwaves are more likely to become stable when symbols are reordered inboth the frequency and the time domains as in FIGS. 18A and 18B, therebymaking it easier to achieve the advantageous effects of the presentinvention. When symbols are ordered in the frequency domain, however,fluctuations in the frequency domain are abrupt, leading to thepossibility of yielding diversity gain. Therefore, reordering in boththe frequency and the time domains is not necessarily always the bestmethod.

FIGS. 19A and 19B show an example of a method of reordering symbols bythe reordering units 1404A and 1404B in FIG. 14, the horizontal axisrepresenting frequency, and the vertical axis representing time, thatdiffers from FIGS. 18A and 18B. FIG. 19A shows the reordering method forsymbols of the modulated signal z1, and FIG. 19B shows the reorderingmethod for symbols of the modulated signal z2. As in FIGS. 18A and 18B,FIGS. 19A and 19B show arrangement of symbols using both the frequencyand the time axes. The difference as compared to FIGS. 18A and 18B isthat, whereas symbols are arranged first in the frequency domain andthen in the time domain in FIGS. 18A and 18B, symbols are arranged firstin the time domain and then in the frequency domain in FIGS. 19A and19B. In FIGS. 19A and 19B, the symbol group 1901 and the symbol group1902 are the symbols for one period (cycle) when using the precodinghopping method.

Note that in FIGS. 18A, 18B, 19A, and 19B, as in FIGS. 16A and 16B, thepresent invention may be similarly embodied, and the advantageous effectof high reception quality achieved, with the symbol arranging method ofthe modulated signal z1 differing from the symbol arranging method ofthe modulated signal z2. Furthermore, in FIGS. 18A, 18B, 19A, and 19B,as in FIGS. 17A and 17B, the present invention may be similarlyembodied, and the advantageous effect of high reception qualityachieved, without arranging the symbols in order.

FIG. 27 shows an example of a method of reordering symbols by thereordering units 1404A and 1404B in FIG. 14, the horizontal axisrepresenting frequency, and the vertical axis representing time, thatdiffers from the above examples. The case of hopping between precodingmatrix regularly over four slots, as in Equations 37-40, is considered.The characteristic feature of FIG. 27 is that symbols are arranged inorder in the frequency domain, but when progressing in the time domain,symbols are cyclically shifted by n symbols (in the example in FIG. 27,n=1). In the four symbols shown in the symbol group 2710 in thefrequency domain in FIG. 27, precoding hops between the precodingmatrices of Equations 37-40.

In this case, symbol #0 is precoded using the precoding matrix inEquation 37, symbol #1 is precoded using the precoding matrix inEquation 38, symbol #2 is precoded using the precoding matrix inEquation 39, and symbol #3 is precoded using the precoding matrix inEquation 40.

Similarly, for the symbol group 2720 in the frequency domain, symbol #4is precoded using the precoding matrix in Equation 37, symbol #5 isprecoded using the precoding matrix in Equation 38, symbol #6 isprecoded using the precoding matrix in Equation 39, and symbol #7 isprecoded using the precoding matrix in Equation 40.

For the symbols at time $1, precoding hops between the above precodingmatrices, but in the time domain, symbols are cyclically shifted.Therefore, precoding hops between precoding matrices for the symbolgroups 2701, 2702, 2703, and 2704 as follows.

In the symbol group 2701 in the time domain, symbol #0 is precoded usingthe precoding matrix in Equation 37, symbol #9 is precoded using theprecoding matrix in Equation 38, symbol #18 is precoded using theprecoding matrix in Equation 39, and symbol #27 is precoded using theprecoding matrix in Equation 40.

In the symbol group 2702 in the time domain, symbol #28 is precodedusing the precoding matrix in Equation 37, symbol #1 is precoded usingthe precoding matrix in Equation 38, symbol #10 is precoded using theprecoding matrix in Equation 39, and symbol #19 is precoded using theprecoding matrix in Equation 40.

In the symbol group 2703 in the time domain, symbol #20 is precodedusing the precoding matrix in Equation 37, symbol #29 is precoded usingthe precoding matrix in Equation 38, symbol #2 is precoded using theprecoding matrix in Equation 39, and symbol #11 is precoded using theprecoding matrix in Equation 40.

In the symbol group 2704 in the time domain, symbol #12 is precodedusing the precoding matrix in Equation 37, symbol #21 is precoded usingthe precoding matrix in Equation 38, symbol #30 is precoded using theprecoding matrix in Equation 39, and symbol #3 is precoded using theprecoding matrix in Equation 40.

The characteristic of FIG. 27 is that, for example focusing on symbol#11, the symbols on either side in the frequency domain at the same time(symbols #10 and #12) are both precoded with a different precodingmatrix than symbol #11, and the symbols on either side in the timedomain in the same carrier (symbols #2 and #20) are both precoded with adifferent precoding matrix than symbol #11. This is true not only forsymbol #11. Any symbol having symbols on either side in the frequencydomain and the time domain is characterized in the same way as symbol#11. As a result, precoding matrices are effectively hopped between, andsince the influence on stable conditions of direct waves is reduced, thepossibility of improved reception quality of data increases.

In FIG. 27, the case of n=1 has been described, but n is not limited inthis way. The present invention may be similarly embodied with n=3.Furthermore, in FIG. 27, when symbols are arranged in the frequencydomain and time progresses in the time domain, the above characteristicis achieved by cyclically shifting the number of the arranged symbol,but the above characteristic may also be achieved by randomly (orregularly) arranging the symbols.

Embodiment 2

In Embodiment 1, regular hopping of the precoding weights as shown inFIG. 6 has been described. In the present embodiment, a method fordesigning specific precoding weights that differ from the precodingweights in FIG. 6 is described.

In FIG. 6, the method for hopping between the precoding weights inEquations 37-40 has been described. By generalizing this method, theprecoding weights may be changed as follows. (The hopping period (cycle)for the precoding weights has four slots, and Equations are listedsimilarly to Equations 37-40.) For symbol number 4i (where i is aninteger greater than or equal to zero):

$\begin{matrix}{{Math}\mspace{14mu} 42} & \; \\{\begin{pmatrix}{z\; 1\;\left( {4\; i} \right)} \\{z\; 2\;\left( {4\; i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{({4\; i})}}}\;} & {\mathbb{e}}^{{j\;{({{\theta_{11}{({4\; i})}} + \lambda})}}\;} \\{\mathbb{e}}^{{j\;{\theta_{21}{({4\; i})}}}\;} & {\mathbb{e}}^{j\;{({{\theta_{21}{({4\; i})}}\; + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {4\; i} \right)} \\{s\; 2\;\left( {4\; i} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 42}\end{matrix}$Here, j is an imaginary unit.For symbol number 4i+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 43}} & \; \\{\begin{pmatrix}{z\; 1\;\left( {{4\; i} + 1} \right)} \\{z\; 2\;\left( {{4\; i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{({{4\; i} + 1})}}}\;} & {\mathbb{e}}^{{j\;{({{\theta_{11}{({{4\; i} + 1})}} + \lambda})}}\;} \\{\mathbb{e}}^{{j\;{\theta_{21}{({{4\; i} + 1})}}}\;} & {\mathbb{e}}^{j\;{({{\theta_{21}{({{4\; i} + 1})}}\; + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {{4\; i} + 1} \right)} \\{s\; 2\;\left( {{4\; i} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 43}\end{matrix}$For symbol number 4i+2:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 44}} & \; \\{\begin{pmatrix}{z\; 1\;\left( {{4\; i} + 2} \right)} \\{z\; 2\;\left( {{4\; i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{({{4\; i} + 2})}}}\;} & {\mathbb{e}}^{{j\;{({{\theta_{11}{({{4\; i} + 2})}} + \lambda})}}\;} \\{\mathbb{e}}^{{j\;{\theta_{21}{({{4\; i} + 2})}}}\;} & {\mathbb{e}}^{j\;{({{\theta_{21}{({{4\; i} + 2})}}\; + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {{4\; i} + 2} \right)} \\{s\; 2\;\left( {{4\; i} + 2} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 44}\end{matrix}$For symbol number 4i+3:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 45}} & \; \\{\begin{pmatrix}{z\; 1\;\left( {{4\; i} + 3} \right)} \\{z\; 2\;\left( {{4\; i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{({{4\; i} + 3})}}}\;} & {\mathbb{e}}^{{j\;{({{\theta_{11}{({{4\; i} + 3})}} + \lambda})}}\;} \\{\mathbb{e}}^{{j\;{\theta_{21}{({{4\; i} + 3})}}}\;} & {\mathbb{e}}^{j\;{({{\theta_{21}{({{4\; i} + 3})}}\; + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {{4\; i} + 3} \right)} \\{s\; 2\;\left( {{4\; i} + 3} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 45}\end{matrix}$From Equations 36 and 41, the received vector R(t)=(r1(t), r2(t))^(T)can be represented as follows.For symbol number 4i:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 46}} & \; \\{\begin{pmatrix}{r\; 1\;\left( {4\; i} \right)} \\{r\; 2\;\left( {4\; i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{h_{11}\left( {4\; i} \right)} & {h_{12}\left( {4\; i} \right)} \\{h_{21}\left( {4\; i} \right)} & {h_{22}\left( {4\; i} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{({4\; i})}}}\;} & {\mathbb{e}}^{{j\;{({{\theta_{11}{({4\; i})}} + \lambda})}}\;} \\{\mathbb{e}}^{{j\;{\theta_{21}{({4\; i})}}}\;} & {\mathbb{e}}^{j\;{({{\theta_{21}{({4\; i})}}\; + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {4\; i} \right)} \\{s\; 2\;\left( {4\; i} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 46}\end{matrix}$For symbol number 4i+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 47}} & \; \\{\begin{pmatrix}{r\; 1\;\left( {{4\; i} + 1} \right)} \\{r\; 2\;\left( {{4\; i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{h_{11}\left( {{4\; i} + 1} \right)} & {h_{12}\left( {{4\; i} + 1} \right)} \\{h_{21}\left( {{4\; i} + 1} \right)} & {h_{22}\left( {{4\; i} + 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{({{4\; i} + 1})}}}\;} & {\mathbb{e}}^{{j\;{({{\theta_{11}{({{4\; i} + 1})}} + \lambda})}}\;} \\{\mathbb{e}}^{{j\;{\theta_{21}{({{4\; i} + 1})}}}\;} & {\mathbb{e}}^{j\;{({{\theta_{21}{({{4\; i} + 1})}}\; + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {{4\; i} + 1} \right)} \\{s\; 2\;\left( {{4\; i} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 47}\end{matrix}$For symbol number 4i+2:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 48}} & \; \\{\begin{pmatrix}{r\; 1\;\left( {{4\; i} + 2} \right)} \\{r\; 2\;\left( {{4\; i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{h_{11}\left( {{4\; i} + 2} \right)} & {h_{12}\left( {{4\; i} + 2} \right)} \\{h_{21}\left( {{4\; i} + 2} \right)} & {h_{22}\left( {{4\; i} + 2} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{({{4\; i} + 2})}}}\;} & {\mathbb{e}}^{{j\;{({{\theta_{11}{({{4\; i} + 2})}} + \lambda})}}\;} \\{\mathbb{e}}^{{j\;{\theta_{21}{({{4\; i} + 2})}}}\;} & {\mathbb{e}}^{j\;{({{\theta_{21}{({{4\; i} + 2})}}\; + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {{4\; i} + 2} \right)} \\{s\; 2\;\left( {{4\; i} + 2} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 48}\end{matrix}$For symbol number 4i+3:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 49}} & \; \\{\begin{pmatrix}{r\; 1\;\left( {{4\; i} + 3} \right)} \\{r\; 2\;\left( {{4\; i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{h_{11}\left( {{4\; i} + 3} \right)} & {h_{12}\left( {{4\; i} + 3} \right)} \\{h_{21}\left( {{4\; i} + 3} \right)} & {h_{22}\left( {{4\; i} + 3} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{({{4\; i} + 3})}}}\;} & {\mathbb{e}}^{{j\;{({{\theta_{11}{({{4\; i} + 3})}} + \lambda})}}\;} \\{\mathbb{e}}^{{j\;{\theta_{21}{({{4\; i} + 3})}}}\;} & {\mathbb{e}}^{j\;{({{\theta_{21}{({{4\; i} + 3})}}\; + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {{4\; i} + 3} \right)} \\{s\; 2\;\left( {{4\; i} + 3} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 49}\end{matrix}$

In this case, it is assumed that only components of direct waves existin the channel elements h₁₁(t), h₁₂(t), h₂₁(t), and h₂₂(t), that theamplitude components of the direct waves are all equal, and thatfluctuations do not occur over time. With these assumptions, Equations46-49 can be represented as follows.

For symbol number 4i:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 50}} & \; \\{\begin{pmatrix}{r\; 1\;\left( {4\; i} \right)} \\{r\; 2\;\left( {4\; i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{({4\; i})}}}\;} & {\mathbb{e}}^{{j\;{({{\theta_{11}{({4\; i})}} + \lambda})}}\;} \\{\mathbb{e}}^{{j\;{\theta_{21}{({4\; i})}}}\;} & {\mathbb{e}}^{j\;{({{\theta_{21}{({4\; i})}}\; + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {4\; i} \right)} \\{s\; 2\;\left( {4\; i} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 50}\end{matrix}$For symbol number 4i+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 51}} & \; \\{\begin{pmatrix}{r\; 1\;\left( {{4\; i} + 1} \right)} \\{r\; 2\;\left( {{4\; i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{({{4\; i} + 1})}}}\;} & {\mathbb{e}}^{{j\;{({{\theta_{11}{({{4\; i} + 1})}} + \lambda})}}\;} \\{\mathbb{e}}^{{j\;{\theta_{21}{({{4\; i} + 1})}}}\;} & {\mathbb{e}}^{j\;{({{\theta_{21}{({{4\; i} + 1})}}\; + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {{4\; i} + 1} \right)} \\{s\; 2\;\left( {{4\; i} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 51}\end{matrix}$For symbol number 4i+2:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 52}} & \; \\{\begin{pmatrix}{r\; 1\;\left( {{4\; i} + 2} \right)} \\{r\; 2\;\left( {{4\; i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\;{\theta_{11}{({{4\; i} + 2})}}}\;} & {\mathbb{e}}^{{j\;{({{\theta_{11}{({{4\; i} + 2})}} + \lambda})}}\;} \\{\mathbb{e}}^{{j\;{\theta_{21}{({{4\; i} + 2})}}}\;} & {\mathbb{e}}^{j\;{({{\theta_{21}{({{4\; i} + 2})}}\; + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\;\left( {{4\; i} + 2} \right)} \\{s\; 2\;\left( {{4\; i} + 2} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 52}\end{matrix}$For symbol number 4i+3:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 53}} & \; \\{\begin{pmatrix}{r\; 1\left( {{4\; i} + 3} \right)} \\{r\; 2\left( {{4\; i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4\; i} + 3})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4\; i} + 3})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4\; i} + 3})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4\; i} + 3})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4\; i} + 3} \right)} \\{s\; 2\left( {{4\; i} + 3} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 53}\end{matrix}$

In Equations 50-53, let A be a positive real number and q be a complexnumber. The values of A and q are determined in accordance with thepositional relationship between the transmission device and thereception device. Equations 50-53 can be represented as follows.

For symbol number 4i:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 54}} & \; \\{\begin{pmatrix}{r\; 1\left( {4\; i} \right)} \\{r\; 2\left( {4\; i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({4\; i})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({4\; i})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({4\; i})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({4\; i})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {4\; i} \right)} \\{s\; 2\left( {4\; i} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 54}\end{matrix}$For symbol number 4i+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 55}} & \; \\{\begin{pmatrix}{r\; 1\left( {{4\; i} + 1} \right)} \\{r\; 2\left( {{4\; i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4\; i} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4\; i} + 1})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4\; i} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4\; i} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4\; i} + 1} \right)} \\{s\; 2\left( {{4\; i} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 55}\end{matrix}$For symbol number 4i+2:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 56}} & \; \\{\begin{pmatrix}{r\; 1\left( {{4\; i} + 2} \right)} \\{r\; 2\left( {{4\; i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4\; i} + 2})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4\; i} + 2})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4\; i} + 2})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4\; i} + 2})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4\; i} + 2} \right)} \\{s\; 2\left( {{4\; i} + 2} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 56}\end{matrix}$For symbol number 4i+3:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 57}} & \; \\{\begin{pmatrix}{r\; 1\left( {{4\; i} + 3} \right)} \\{r\; 2\left( {{4\; i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{4\; i} + 3})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{4\; i} + 3})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{4\; i} + 3})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{4\; i} + 3})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{4\; i} + 3} \right)} \\{s\; 2\left( {{4\; i} + 3} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 57}\end{matrix}$

As a result, when q is represented as follows, a signal component basedon one of s1 and s2 is no longer included in r1 and r2, and thereforeone of the signals s1 and s2 can no longer be obtained.

For symbol number 4i:Math 58q=−A _(e) ^(j(θ) ¹¹ ^((4i)−θ) ²¹ ^((4i))) ,−A _(e) ^(j(θ) ¹¹ ^((4i)−θ)²¹ ^((4i)−δ))  Equation 58For symbol number 4i+1:Math 59q=−A _(e) ^(j(θ) ¹¹ ^((4i+1)−θ) ²¹ ^((4i+1))) ,−A _(e) ^(j(θ) ¹¹^((4i+1)−θ) ²¹ ^((4i+1)−δ))  Equation 59For symbol number 4i+2:Math 60q=−A _(e) ^(j(θ) ¹¹ ^((4i+2)−θ) ²¹ ^((4i+2))) ,−A _(e) ^(j(θ) ¹¹^((4i+2)−θ) ²¹ ^((4i+2)−δ))  Equation 60For symbol number 4i+3:Math 61q=−A _(e) ^(j(θ) ¹¹ ^((4i+3)−θ) ²¹ ^((4i+3))) ,−A _(e) ^(j(θ) ¹¹^((4i+3)−θ) ²¹ ^((4i+3)−δ))  Equation 61

In this case, if q has the same solution in symbol numbers 4i, 4i+1,4i+2, and 4i+3, then the channel elements of the direct waves do notgreatly fluctuate. Therefore, a reception device having channel elementsin which the value of q is equivalent to the same solution can no longerobtain excellent reception quality for any of the symbol numbers.Therefore, it is difficult to achieve the ability to correct errors,even if error correction codes are introduced. Accordingly, for q not tohave the same solution, the following condition is necessary fromEquations 58-61 when focusing on one of two solutions of q which doesnot include δ.Math 62e ^(j(θ) ¹¹ ^((4i+x)−θ) ²¹ ^((4i+x))) ≠e ^(j(θ) ¹¹ ^((4i+y)−θ) ²¹^((4i+y))) for ∀x,∀y(x≠y;x,y=0,1,2,3)  Condition #1(x is 0, 1, 2, 3; y is 0, 1, 2, 3; and x y.)

In an example fulfilling Condition #1, values are set as follows:

Example #1

(1) θ₁₁ (4i)=θ₁₁ (4i+1)=θ₁₁ (4i+2)=θ₁₁ (4i+3)=0 radians,

(2) θ₂₁ (4i)=0 radians,

(3) θ₂₁ (4i+1)=π/2 radians,

(4) θ₂₁ (4i+2)=π radians, and

(5) θ₂₁ (4i+3)=3π/2 radians.

(The above is an example. It suffices for one each of zero radians, π/2radians, π radians, and 3π/2 radians to exist for the set (θ₂₁(4i),θ₂₁(4i+1), θ₂₁(4i+2), θ₂₁(4i+3)).) In this case, in particular undercondition (1), there is no need to perform signal processing (rotationprocessing) on the baseband signal S1(t), which therefore offers theadvantage of a reduction in circuit size. Another example is to setvalues as follows.

Example #2

(6) θ₁₁(4i)=0 radians,

(7) θ₁₁(4i+1)=π/2 radians,

(8) θ₁₁(4i+2)=π radians,

(9) θ₁₁(4i+3)=3π/2 radians, and

(10) θ₂₁(4i)=θ₂₁(4i+1)=θ₂₁(4i+2)=θ₂₁(4i+3)=0 radians.

(The above is an example. It suffices for one each of zero radians, π/2radians, π radians, and 3π/2 radians to exist for the set (θ₁₁(4i),θ₁₁(4i+1), θ₁₁(4i+2), θ₁₁(4i+3)).) In this case, in particular undercondition (6), there is no need to perform signal processing (rotationprocessing) on the baseband signal S2(t), which therefore offers theadvantage of a reduction in circuit size. Yet another example is asfollows.

Example #3

(11) θ₁₁(4i)=θ₁₁(4i+1)=θ₁₁(4i+2)=θ₁₁(4i+3)=0 radians,

(12) θ₂₁(4i)=0 radians,

(13) θ₂₁(4i+1)=π/4 radians,

(14) θ₂₁(4i+2)=π/2 radians, and

(15) θ₂₁(4i+3)=3π/4 radians.

(The above is an example. It suffices for one each of zero radians, π/4radians, π/2 radians, and 3π/4 radians to exist for the set (θ₂₁(4i),θ₂₁(4i+1), θ₂₁(4i+2), θ₂₁(4i+³)).)

Example #4

(16) θ₁₁(4i)=0 radians,

(17) θ₁₁(4i+1)=π/4 radians,

(18) θ₁₁(4i+2)=π/2 radians,

(19) θ₁₁(4i+3)=3π/4 radians, and

(20) θ₂₁(4i)=θ₂₁(4i+1)=θ₂₁(4i+2)=θ₂₁(4i+3)=0 radians.

(The above is an example. It suffices for one each of zero radians, π/4radians, π/2 radians, and 3π/4 radians to exist for the set (θ₁₁(4i),θ₁₁(4i+1), θ₁₁(4i+2), θ₁₁(4i+³)).)

While four examples have been shown, the method of satisfying Condition#1 is not limited to these examples.

Next, design requirements for not only θ₁₁ and θ₁₂, but also for λ and δare described. It suffices to set λ to a certain value; it is thennecessary to establish requirements for δ. The following describes thedesign method for δ when λ is set to zero radians.

In this case, by defining δ so that π/2 radians≦|δ|≦π radians, excellentreception quality is achieved, particularly in an LOS environment.

Incidentally, for each of the symbol numbers 4i, 4i+1, 4i+2, and 4i+3,two points q exist where reception quality becomes poor. Therefore, atotal of 2×4=8 such points exist. In an LOS environment, in order toprevent reception quality from degrading in a specific receptionterminal, these eight points should each have a different solution. Inthis case, in addition to Condition #1, Condition #2 is necessary.Math 63e ^(j(θ) ¹¹ ^((4i+x)−θ) ²¹ ^((4i+x))) ≠e ^(j(θ) ¹¹ ^((4i+y)−θ) ²¹^((4i+y)−δ)) for ∀x,∀y(x≠y;x,y=0,1,2,3)ande ^(j(θ) ¹¹ ^((4i+x)−θ) ²¹ ^((4i+x)−δ)) ≠e ^(j(θ) ¹¹ ^((4i+y)−θ) ²¹^((4i+y)−δ)) for ∀x,∀y(x≠y;x,y=0,1,2,3)  Condition #2

Additionally, the phase of these eight points should be evenlydistributed (since the phase of a direct wave is considered to have ahigh probability of even distribution). The following describes thedesign method for δ to satisfy this requirement.

In the case of example #1 and example #2, the phase becomes even at thepoints at which reception quality is poor by setting δ to ±3π/4 radians.For example, letting δ be 3π/4 radians in example #1 (and letting A be apositive real number), then each of the four slots, points at whichreception quality becomes poor exist once, as shown in FIG. 20. In thecase of example #3 and example #4, the phase becomes even at the pointsat which reception quality is poor by setting δ to ±π radians. Forexample, letting δ be π radians in example #3, then in each of the fourslots, points at which reception quality becomes poor exist once, asshown in FIG. 21. (If the element q in the channel matrix H exists atthe points shown in FIGS. 20 and 21, reception quality degrades.)

With the above structure, excellent reception quality is achieved in anLOS environment. Above, an example of changing precoding weights in afour-slot period (cycle) is described, but below, changing precodingweights in an N-slot period (cycle) is described. Making the sameconsiderations as in Embodiment 1 and in the above description,processing represented as below is performed on each symbol number.

For symbol number Ni (where i is an integer greater than or equal tozero):

$\begin{matrix}{{Math}\mspace{14mu} 64} & \; \\{\begin{pmatrix}{z\; 1({Ni})} \\{z\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 62}\end{matrix}$Here, j is an imaginary unit.For symbol number Ni+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 65}} & \; \\{\begin{pmatrix}{z\; 1\left( {{Ni} + 1} \right)} \\{z\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 63}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 66}} & \; \\{\begin{pmatrix}{z\; 1\left( {{Ni} + k} \right)} \\{z\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 64}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 67}} & \; \\{\begin{pmatrix}{z\; 1\left( {{Ni} + N - 1} \right)} \\{z\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 65}\end{matrix}$Accordingly, r1 and r2 are represented as follows.For symbol number Ni (where i is an integer greater than or equal tozero):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 68}} & \; \\{\begin{pmatrix}{r\; 1({Ni})} \\{r\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{h_{11}({Ni})} & {h_{12}({Ni})} \\{h_{21}({Ni})} & {h_{22}({Ni})}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 66}\end{matrix}$Here, j is an imaginary unit.For symbol number Ni+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 69}} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + 1} \right)} \\{r\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{h_{11}\left( {{Ni} + 1} \right)} & {h_{12}\left( {{Ni} + 1} \right)} \\{h_{21}\left( {{Ni} + 1} \right)} & {h_{22}\left( {{Ni} + 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 67}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 70}} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + k} \right)} \\{r\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{h_{11}\left( {{Ni} + k} \right)} & {h_{12}\left( {{Ni} + k} \right)} \\{h_{21}\left( {{Ni} + k} \right)} & {h_{22}\left( {{Ni} + k} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 68}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 71}} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + N - 1} \right)} \\{r\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{h_{11}\left( {{Ni} + N - 1} \right)} & {h_{12}\left( {{Ni} + N - 1} \right)} \\{h_{21}\left( {{Ni} + N - 1} \right)} & {h_{22}\left( {{Ni} + N - 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 69}\end{matrix}$

In this case, it is assumed that only components of direct waves existin the channel elements h₁₁(t), h₁₂(t), h₂₁(t), and h₂₂(t), that theamplitude components of the direct waves are all equal, and thatfluctuations do not occur over time. With these assumptions, Equations66-69 can be represented as follows.

For symbol number Ni (where i is an integer greater than or equal tozero):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 72}} & \; \\{\begin{pmatrix}{r\; 1({Ni})} \\{r\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 70}\end{matrix}$

Here, j is an imaginary unit.

For symbol number Ni+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 73}} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + 1} \right)} \\{r\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 71}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 74}} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + k} \right)} \\{r\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + k})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 72}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 75}} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + N - 1} \right)} \\{r\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + N - 1})}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 73}\end{matrix}$

In Equations 70-73, let A be a real number and q be a complex number.The values of A and q are determined in accordance with the positionalrelationship between the transmission device and the reception device.Equations 70-73 can be represented as follows.

For symbol number Ni (where i is an integer greater than or equal tozero):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 76}} & \; \\{\begin{pmatrix}{r\; 1({Ni})} \\{r\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({Ni})}} & {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({Ni})}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 74}\end{matrix}$Here, j is an imaginary unit.For symbol number Ni+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 77}} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + 1} \right)} \\{r\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + 1})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 75}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 78}} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + k} \right)} \\{r\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 76}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 79}} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + N - 1} \right)} \\{r\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 77}\end{matrix}$

As a result, when q is represented as follows, a signal component basedon one of s1 and s2 is no longer included in r1 and r2, and thereforeone of the signals s1 and s2 can no longer be obtained.

For symbol number Ni (where i is an integer greater than or equal tozero):Math 80q=−A _(e) ^(j(θ) ¹¹ ^((Ni)−θ) ²¹ ^((Ni))) ,−A _(e) ^(j(θ) ¹¹ ^((Ni)−θ)²¹ ^((Ni)−δ))  Equation 78For symbol number Ni+1:Math 81q=−A _(e) ^(j(θ) ¹¹ ^((Ni+1)−θ) ²¹ ^((Ni+1))) ,−A _(e) ^(j(θ) ¹¹^((Ni+1)−θ) ²¹ ^((Ni+1)−δ))  Equation 79

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, N−1):Math 82q=−A _(e) ^(j(θ) ¹¹ ^((Ni+k)−θ) ²¹ ^((Ni+k))) ,−A _(e) ^(j(θ) ¹¹^((Ni+k)−θ) ²¹ ^((Ni+k)−δ))  Equation 80

Furthermore, for symbol number Ni+N−1:Math 83q=−A _(e) ^(j(θ) ¹¹ ^((Ni+N−1)−θ) ²¹ ^((Ni+N−1))) ,−A _(e) ^(j(θ) ¹¹^((Ni+N−1)−θ) ²¹ ^((Ni+N−1)−δ))  Equation 81

In this case, if q has the same solution in symbol numbers Ni throughNi+N−1, then since the channel elements of the direct waves do notgreatly fluctuate, a reception device having channel elements in whichthe value of q is equivalent to this same solution can no longer obtainexcellent reception quality for any of the symbol numbers. Therefore, itis difficult to achieve the ability to correct errors, even if errorcorrection codes are introduced. Accordingly, for q not to have the samesolution, the following condition is necessary from Equations 78-81 whenfocusing on one of two solutions of q which does not include δ.Math 84e ^(j(θ) ¹¹ ^((Ni+x)−θ) ²¹ ^((Ni+x))) ≠e ^(j(θ) ¹¹ ^((Ni+y)−θ) ²¹^((Ni+y))) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #3(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Next, design requirements for not only θ₁₁ and θ₁₂, but also for λ and δare described. It suffices to set λ to a certain value; it is thennecessary to establish requirements for δ. The following describes thedesign method for δ when λ is set to zero radians.

In this case, similar to the method of changing the precoding weights ina four-slot period (cycle), by defining δ so that π/2 radians≦|δ|≦πradians, excellent reception quality is achieved, particularly in an LOSenvironment.

In each symbol number Ni through Ni+N−1, two points labeled q existwhere reception quality becomes poor, and therefore 2N such pointsexist. In an LOS environment, in order to achieve excellentcharacteristics, these 2N points should each have a different solution.In this case, in addition to Condition #3, Condition #4 is necessary.Math 85e ^(j(θ) ¹¹ ^((Ni+x)−θ) ²¹ ^((Ni+x))) ≠e ^(j(θ) ¹¹ ^((Ni+y)−θ) ²¹^((Ni+y)−δ)) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)ande ^(j(θ) ¹¹ ^((Ni+x)−θ) ²¹ ^((Ni+x)−δ)) ≠e ^(j(θ) ¹¹ ^((Ni+y)−θ) ²¹^((Ni+y)−δ)) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #4

Additionally, the phase of these 2N points should be evenly distributed(since the phase of a direct wave at each reception device is consideredto have a high probability of even distribution).

As described above, when a transmission device transmits a plurality ofmodulated signals from a plurality of antennas in a MIMO system, theadvantageous effect of improved transmission quality, as compared toconventional spatial multiplexing MIMO, is achieved in an LOSenvironment in which direct waves dominate by hopping between precodingweights regularly over time.

In the present embodiment, the structure of the reception device is asdescribed in Embodiment 1, and in particular with regards to thestructure of the reception device, operations have been described for alimited number of antennas, but the present invention may be embodied inthe same way even if the number of antennas increases. In other words,the number of antennas in the reception device does not affect theoperations or advantageous effects of the present embodiment.Furthermore, in the present embodiment, similar to Embodiment 1, theerror correction codes are not limited.

In the present embodiment, in contrast with Embodiment 1, the method ofchanging the precoding weights in the time domain has been described. Asdescribed in Embodiment 1, however, the present invention may besimilarly embodied by changing the precoding weights by using amulti-carrier transmission method and arranging symbols in the frequencydomain and the frequency-time domain. Furthermore, in the presentembodiment, symbols other than data symbols, such as pilot symbols(preamble, unique word, and the like), symbols for control information,and the like, may be arranged in the frame in any way.

Embodiment 3

In Embodiment 1 and Embodiment 2, the method of regularly hoppingbetween precoding weights has been described for the case where theamplitude of each element in the precoding weight matrix is equivalent.In the present embodiment, however, an example that does not satisfythis condition is described.

For the sake of contrast with Embodiment 2, the case of changingprecoding weights over an N-slot period (cycle) is described. Making thesame considerations as in Embodiment 1 and Embodiment 2, processingrepresented as below is performed on each symbol number. Let β be apositive real number, and β #1. For symbol number Ni (where i is aninteger greater than or equal to zero):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 86}} & \; \\{\begin{pmatrix}{z\; 1({Ni})} \\{z\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({Ni})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{j\;{\theta_{21}{({Ni})}}}} & {\mathbb{e}}^{j({{\theta_{21}{({Ni})}} + \lambda + \delta}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 82}\end{matrix}$

Here, j is an imaginary unit.

For symbol number Ni+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 87}} & \; \\{\begin{pmatrix}{z\; 1\left( {{Ni} + 1} \right)} \\{z\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + 1})}} & {\beta \times {\mathbb{e}}^{j({{\theta_{11}{({{Ni} + 1})}} + \lambda}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 83}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 88}} & \; \\{\begin{pmatrix}{z\; 1\left( {{Ni} + k} \right)} \\{z\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + k})}} & {\beta \times {\mathbb{e}}^{j({{\theta_{11}{({{Ni} + k})}} + \lambda}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 84}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 89}} & \; \\{\begin{pmatrix}{z\; 1\left( {{Ni} + N - 1} \right)} \\{z\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{Ni} + N - 1})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 85}\end{matrix}$

Accordingly, r1 and r2 are represented as follows.

For symbol number Ni (where i is an integer greater than or equal tozero):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 90}} & \; \\{\begin{pmatrix}{r\; 1({Ni})} \\{r\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}({Ni})} & {h_{12}({Ni})} \\{h_{21}({Ni})} & {h_{22}({Ni})}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({Ni})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 86}\end{matrix}$

Here, j is an imaginary unit.

For symbol number Ni+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 91}} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + 1} \right)} \\{r\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{Ni} + 1} \right)} & {h_{12}\left( {{Ni} + 1} \right)} \\{h_{21}\left( {{Ni} + 1} \right)} & {h_{22}\left( {{Ni} + 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 87}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 92}} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + k} \right)} \\{r\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{Ni} + k} \right)} & {h_{12}\left( {{Ni} + k} \right)} \\{h_{21}\left( {{Ni} + k} \right)} & {h_{22}\left( {{Ni} + k} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + k})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 88}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+N−1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 93}} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + N - 1} \right)} \\{r\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{Ni} + N - 1} \right)} & {h_{12}\left( {{Ni} + N - 1} \right)} \\{h_{21}\left( {{Ni} + N - 1} \right)} & {h_{22}\left( {{Ni} + N - 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + N - 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 89}\end{matrix}$

In this case, it is assumed that only components of direct waves existin the channel elements h₁₁(t), h₁₂(t), h₂₁(t), and h₂₂(t), that theamplitude components of the direct waves are all equal, and thatfluctuations do not occur over time. With these assumptions, Equations86-89 can be represented as follows. For symbol number Ni (where i is aninteger greater than or equal to zero):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 94}} & \; \\{\begin{pmatrix}{r\; 1({Ni})} \\{r\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({Ni})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 90}\end{matrix}$

Here, j is an imaginary unit.

For symbol number Ni+1:

$\begin{matrix}{{Math}\mspace{14mu} 95} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + 1} \right)} \\{r\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 91}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{{Math}\mspace{14mu} 96} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + k} \right)} \\{r\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + k})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 92}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

$\begin{matrix}{{Math}\mspace{14mu} 97} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + N - 1} \right)} \\{r\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + N - 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 93}\end{matrix}$

In Equations 90-93, let A be a real number and q be a complex number.Equations 90-93 can be represented as follows.

For symbol number Ni (where i is an integer greater than or equal tozero):

$\begin{matrix}{{Math}\mspace{14mu} 98} & \; \\{\begin{pmatrix}{r\; 1({Ni})} \\{r\; 2({Ni})}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\left( {A\;{\mathbb{e}}^{j\; 0}\mspace{31mu} q} \right)\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({Ni})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({Ni})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({Ni})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1({Ni})} \\{s\; 2({Ni})}\end{pmatrix}}} & {{Equation}\mspace{14mu} 94}\end{matrix}$

Here, j is an imaginary unit.

For symbol number Ni+1:

$\begin{matrix}{{Math}\mspace{14mu} 99} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + 1} \right)} \\{r\; 2\left( {{Ni} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\left( {A\;{\mathbb{e}}^{j\; 0}\mspace{31mu} q} \right)\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + 1} \right)} \\{s\; 2\left( {{Ni} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 95}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{{Math}\mspace{14mu} 100} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + k} \right)} \\{r\; 2\left( {{Ni} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\left( {A\;{\mathbb{e}}^{j\; 0}\mspace{31mu} q} \right)\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + k})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + k} \right)} \\{s\; 2\left( {{Ni} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 96}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

$\begin{matrix}{{Math}\mspace{14mu} 101} & \; \\{\begin{pmatrix}{r\; 1\left( {{Ni} + N - 1} \right)} \\{r\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\left( {A\;{\mathbb{e}}^{j\; 0}\mspace{31mu} q} \right)\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{Ni} + N - 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{Ni} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{Ni} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{Ni} + N - 1} \right)} \\{s\; 2\left( {{Ni} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 97}\end{matrix}$

As a result, when q is represented as follows, one of the signals s1 ands2 can no longer be obtained.

For symbol number Ni (where i is an integer greater than or equal tozero):

$\begin{matrix}{{Math}\mspace{14mu} 102} & \; \\{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} - {\theta_{21}{({Ni})}}})}}}},{{- A}\;{\beta\mathbb{e}}^{j{({{\theta_{11}{({Ni})}} - {\theta_{21}{({Ni})}} - \delta})}}}} & {{Equation}\mspace{14mu} 98}\end{matrix}$For symbol number Ni+1:

$\begin{matrix}{{Math}\mspace{14mu} 103} & \; \\{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} - {\theta_{21}{({{Ni} + 1})}}})}}}},{{- A}\;{\beta\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + 1})}} - {\theta_{21}{({{Ni} + 1})}} - \delta})}}}} & {{Equation}\mspace{14mu} 99}\end{matrix}$

When generalized, this equation is as follows.

For symbol number Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{{Math}\mspace{14mu} 104} & \; \\{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} - {\theta_{21}{({{Ni} + k})}}})}}}},{{- A}\;{\beta\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + k})}} - {\theta_{21}{({{Ni} + k})}} - \delta})}}}} & {{Equation}\mspace{14mu} 100}\end{matrix}$

Furthermore, for symbol number Ni+N−1:

$\begin{matrix}{{Math}\mspace{14mu} 105} & \; \\{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} - {\theta_{21}{({{Ni} + N - 1})}}})}}}},{{- A}\;{\beta\mathbb{e}}^{j{({{\theta_{11}{({{Ni} + N - 1})}} - {\theta_{21}{({{Ni} + N - 1})}} - \delta})}}}} & {{Equation}\mspace{14mu} 101}\end{matrix}$

In this case, if q has the same solution in symbol numbers Ni throughNi+N−1, then since the channel elements of the direct waves do notgreatly fluctuate, excellent reception quality can no longer be obtainedfor any of the symbol numbers. Therefore, it is difficult to achieve theability to correct errors, even if error correction codes areintroduced. Accordingly, for q not to have the same solution, thefollowing condition is necessary from Equations 98-101 when focusing onone of two solutions of q which does not include δ.Math 106e ^(j(θ) ¹¹ ^((Ni+x)−θ) ²¹ ^((Ni+x))) ≠e ^(j(θ) ¹¹ ^((Ni+y)−θ) ²¹^((Ni+y))) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #5(x is 0, 1, 2, . . . , N−2,N−1; y is 0, 1, 2, . . . , N−2,N−1; and x≠y.

Next, design requirements for not only θ₁₁ and θ₁₂, but also for λ and δare described. It suffices to set λ to a certain value; it is thennecessary to establish requirements for δ. The following describes thedesign method for δ when λ is set to zero radians.

In this case, similar to the method of changing the precoding weights ina four-slot period (cycle), by defining δ so that π/2 radians≦|δ|≦πradians, excellent reception quality is achieved, particularly in an LOSenvironment.

In each of symbol numbers Ni through Ni+N−1, two points q exist wherereception quality becomes poor, and therefore 2N such points exist. Inan LOS environment, in order to achieve excellent characteristics, these2N points should each have a different solution. In this case, inaddition to Condition #5, considering that β is a positive real number,and β≠1, Condition #6 is necessary.Math 107e ^(j(θ) ¹¹ ^((Ni+x)−θ) ²¹ ^((Ni+x)−δ)) ≠e ^(j(θ) ¹¹ ^((Ni+y)−θ) ²¹^((Ni+y)−δ)) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #6

As described above, when a transmission device transmits a plurality ofmodulated signals from a plurality of antennas in a MIMO system, theadvantageous effect of improved transmission quality, as compared toconventional spatial multiplexing MIMO, is achieved in an LOSenvironment in which direct waves dominate by hopping between precodingweights regularly over time.

In the present embodiment, the structure of the reception device is asdescribed in Embodiment 1, and in particular with regards to thestructure of the reception device, operations have been described for alimited number of antennas, but the present invention may be embodied inthe same way even if the number of antennas increases. In other words,the number of antennas in the reception device does not affect theoperations or advantageous effects of the present embodiment.Furthermore, in the present embodiment, similar to Embodiment 1, theerror correction codes are not limited.

In the present embodiment, in contrast with Embodiment 1, the method ofchanging the precoding weights in the time domain has been described. Asdescribed in Embodiment 1, however, the present invention may besimilarly embodied by changing the precoding weights by using amulti-carrier transmission method and arranging symbols in the frequencydomain and the frequency-time domain. Furthermore, in the presentembodiment, symbols other than data symbols, such as pilot symbols(preamble, unique word, and the like), symbols for control information,and the like, may be arranged in the frame in any way.

Embodiment 4

In Embodiment 3, the method of regularly hopping between precodingweights has been described for the example of two types of amplitudesfor each element in the precoding weight matrix, 1 and 3.

In this case, the following is ignored.

$\begin{matrix}\frac{1}{\sqrt{\beta^{2} + 1}} & {{Math}\mspace{14mu} 108}\end{matrix}$

Next, the example of changing the value of β by slot is described. Forthe sake of contrast with Embodiment 3, the case of changing precodingweights over a 2×N-slot period (cycle) is described.

Making the same considerations as in Embodiment 1, Embodiment 2, andEmbodiment 3, processing represented as below is performed on symbolnumbers. Let β be a positive real number, and β≠1. Furthermore, let α bea positive real number, and α#β.

For symbol number 2Ni (where i is an integer greater than or equal tozero):

$\begin{matrix}{{Math}\mspace{14mu} 109} & \; \\{\begin{pmatrix}{z\; 1\left( {2\;{Ni}} \right)} \\{z\; 2\left( {2\;{Ni}} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({2\;{Ni}})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({2\;{Ni}})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({2\;{Ni}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({2\;{Ni}})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {2\;{Ni}} \right)} \\{s\; 2\left( {2\;{Ni}} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 102}\end{matrix}$Here, j is an imaginary unit.For symbol number 2Ni+1:

$\begin{matrix}{{Math}\mspace{14mu} 110} & \; \\{\begin{pmatrix}{z\; 1\left( {{2\;{Ni}} + 1} \right)} \\{z\; 2\left( {{2\;{Ni}} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2\;{Ni}} + 1})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 103}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{{Math}\mspace{14mu} 111} & \; \\{\begin{pmatrix}{z\; 1\left( {{2\;{Ni}} + k} \right)} \\{z\; 2\left( {{2\;{Ni}} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({{2\;{Ni}} + k})}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + k} \right)} \\{s\; 2\left( {{2\;{Ni}} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 104}\end{matrix}$

Furthermore, for symbol number 2Ni+N−1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 112}} & \; \\{\begin{pmatrix}{z\; 1\left( {{2\;{Ni}} + N - 1} \right)} \\{z\; 2\left( {{2\;{Ni}} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + N - 1})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N - 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 105}\end{matrix}$

For symbol number 2Ni+N (where i is an integer greater than or equal tozero):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 113}} & \; \\{\begin{pmatrix}{z\; 1\left( {{2\;{Ni}} + N} \right)} \\{z\; 2\left( {{2\;{Ni}} + N} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + N})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + N})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + N})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + N})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N} \right)} \\{s\; 2\left( {{2\;{Ni}} + N} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 106}\end{matrix}$

Here, j is an imaginary unit.

For symbol number 2Ni+N+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 114}} & \; \\{\begin{pmatrix}{z\; 1\left( {{2\;{Ni}} + N + 1} \right)} \\{z\; 2\left( {{2\;{Ni}} + N + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + N + 1})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + N + 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + N + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + N + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N + 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + N + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 107}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+N+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 115}} & \; \\{\begin{pmatrix}{z\; 1\left( {{2\;{Ni}} + N + k} \right)} \\{z\; 2\left( {{2\;{Ni}} + N + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + N + k})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + N + k})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + N + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + N + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N + k} \right)} \\{s\; 2\left( {{2\;{Ni}} + N + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 108}\end{matrix}$

Furthermore, for symbol number 2Ni+2N−1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 116}} & \; \\{\begin{pmatrix}{z\; 1\left( {{2\;{Ni}} + {2N} - 1} \right)} \\{z\; 2\left( {{2\;{Ni}} + {2N} - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + {2N} - 1})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + {2N} - 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + {2N} - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + {2N} - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + {2N} - 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + {2N} - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 109}\end{matrix}$

Accordingly, r1 and r2 are represented as follows.

For symbol number 2Ni (where i is an integer greater than or equal tozero):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 117}} & \; \\{\begin{pmatrix}{r\; 1\left( {2\;{Ni}} \right)} \\{r\; 2\left( {2\;{Ni}} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {2\;{Ni}} \right)} & {h_{12}\left( {2\;{Ni}} \right)} \\{h_{21}\left( {2\;{Ni}} \right)} & {h_{22}\left( {2\;{Ni}} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({2\;{Ni}})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({2\;{Ni}})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({2\;{Ni}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({2\;{Ni}})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {2\;{Ni}} \right)} \\{s\; 2\left( {2\;{Ni}} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 110}\end{matrix}$

Here, j is an imaginary unit.

For symbol number 2Ni+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 118}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + 1} \right)} \\{r\; 2\left( {{2\;{Ni}} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2\;{Ni}} + 1} \right)} & {h_{12}\left( {{2\;{Ni}} + 1} \right)} \\{h_{21}\left( {{2\;{Ni}} + 1} \right)} & {h_{22}\left( {{2\;{Ni}} + 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + 1})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 111}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 119}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + k} \right)} \\{r\; 2\left( {{2\;{Ni}} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2\;{Ni}} + k} \right)} & {h_{12}\left( {{2\;{Ni}} + k} \right)} \\{h_{21}\left( {{2\;{Ni}} + k} \right)} & {h_{22}\left( {{2\;{Ni}} + k} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + k})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + k} \right)} \\{s\; 2\left( {{2\;{Ni}} + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 112}\end{matrix}$

Furthermore, for symbol number 2Ni+N−1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 120}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + N - 1} \right)} \\{r\; 2\left( {{2\;{Ni}} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2\;{Ni}} + N - 1} \right)} & {h_{12}\left( {{2\;{Ni}} + N - 1} \right)} \\{h_{21}\left( {{2\;{Ni}} + N - 1} \right)} & {h_{22}\left( {{2\;{Ni}} + N - 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + N - 1})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N - 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + N - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 113}\end{matrix}$For symbol number 2Ni+N (where i is an integer greater than or equal tozero):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 121}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + N} \right)} \\{r\; 2\left( {{2\;{Ni}} + N} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2\;{Ni}} + N} \right)} & {h_{12}\left( {{2\;{Ni}} + N} \right)} \\{h_{21}\left( {{2\;{Ni}} + N} \right)} & {h_{22}\left( {{2\;{Ni}} + N} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + N})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + N})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + N})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + N})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N} \right)} \\{s\; 2\left( {{2\;{Ni}} + N} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 114}\end{matrix}$Here, j is an imaginary unit.For symbol number 2Ni+N+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 122}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + N + 1} \right)} \\{r\; 2\left( {{2\;{Ni}} + N + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2\;{Ni}} + N + 1} \right)} & {h_{12}\left( {{2\;{Ni}} + N + 1} \right)} \\{h_{21}\left( {{2\;{Ni}} + N + 1} \right)} & {h_{22}\left( {{2\;{Ni}} + N + 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + N + 1})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + N + 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + N + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + N + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N + 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + N + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 115}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+N+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 123}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + N + k} \right)} \\{r\; 2\left( {{2\;{Ni}} + N + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2\;{Ni}} + N + k} \right)} & {h_{12}\left( {{2\;{Ni}} + N + k} \right)} \\{h_{21}\left( {{2\;{Ni}} + N + k} \right)} & {h_{22}\left( {{2\;{Ni}} + N + k} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + N + k})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + N + k})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + N + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + N + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N + k} \right)} \\{s\; 2\left( {{2\;{Ni}} + N + k} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 116}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+2N−1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 124}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + {2\; N} - 1} \right)} \\{r\; 2\left( {{2\;{Ni}} + {2\; N} - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{h_{11}\left( {{2\;{Ni}} + {2\; N} - 1} \right)} & {h_{12}\left( {{2\;{Ni}} + {2\; N} - 1} \right)} \\{h_{21}\left( {{2\;{Ni}} + {2\; N} - 1} \right)} & {h_{22}\left( {{2\;{Ni}} + {2\; N} - 1} \right)}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + {2\; N} - 1})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + {2\; N} - 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + {2\; N} - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + {2\; N} - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + {2\; N} - 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + {2\; N} - 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 117}\end{matrix}$

In this case, it is assumed that only components of direct waves existin the channel elements h₁₁(t), h₁₂(t), h₂₁(t), and h₂₂(t), that theamplitude components of the direct waves are all equal, and thatfluctuations do not occur over time. With these assumptions, Equations110-117 can be represented as follows.

For symbol number 2Ni (where i is an integer greater than or equal tozero):

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 125}} & \; \\{\begin{pmatrix}{r\; 1\left( {2\;{Ni}} \right)} \\{r\; 2\left( {2\;{Ni}} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({2\;{Ni}})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({2\;{Ni}})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({2\;{Ni}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({2\;{Ni}})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {2\;{Ni}} \right)} \\{s\; 2\left( {2\;{Ni}} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 118}\end{matrix}$

Here, j is an imaginary unit.

For symbol number 2Ni+1:

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 126}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + 1} \right)} \\{r\; 2\left( {{2\;{Ni}} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + 1})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + 1} \right)}\end{pmatrix}}} & {{Equation}\mspace{14mu} 119}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 120}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + k} \right)} \\{r\; 2\left( {{2\;{Ni}} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + k})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + k} \right)} \\{s\; 2\left( {{2\;{Ni}} + k} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 127}\end{matrix}$Furthermore, for symbol number 2Ni+N−1:

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 121}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + N - 1} \right)} \\{r\; 2\left( {{2\;{Ni}} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + N - 1})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N - 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + N - 1} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 128}\end{matrix}$For symbol number 2Ni+N (where i is an integer greater than or equal tozero):

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 122}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + N} \right)} \\{r\; 2\left( {{2\;{Ni}} + N} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + N})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + N})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + N})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + N})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N} \right)} \\{s\; 2\left( {{2\;{Ni}} + N} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 129}\end{matrix}$

Here, j is an imaginary unit.

For symbol number 2Ni+N+1:

$\begin{matrix}{\mspace{76mu}{{Equation}\mspace{14mu} 123}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + N - 1} \right)} \\{r\; 2\left( {{2\;{Ni}} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\;{Ni}} + N + 1})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + N + 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\;{Ni}} + N + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\;{Ni}} + N + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N + 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + N + 1} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 130}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+N+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 124}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + N + k} \right)} \\{r\; 2\left( {{2\;{Ni}} + N + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\; N\; i} + N + k})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\; N\; i} + N + k})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\; N\; i} + N + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\; N\; i} + N + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N + k} \right)} \\{s\; 2\left( {{2\;{Ni}} + N + k} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 131}\end{matrix}$

Furthermore, for symbol number 2Ni+2N−1:

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 125}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + {2\; N} - 1} \right)} \\{r\; 2\left( {{2\;{Ni}} + {2\; N} - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\mspace{11mu} N\; i} + {2\; N} - 1})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\mspace{11mu} N\; i} + {2\; N} - 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\mspace{11mu} N\; i} + {2\; N} - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\mspace{11mu} N\; i} + {2\; N} - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + {2\; N} - 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + {2\; N} - 1} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 132}\end{matrix}$

In Equations 118-125, let A be a real number and q be a complex number.Equations 118-125 can be represented as follows.

For symbol number 2Ni (where i is an integer greater than or equal tozero):

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 126}} & \; \\{\begin{pmatrix}{r\; 1\left( {2\;{Ni}} \right)} \\{r\; 2\left( {2\;{Ni}} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({2\mspace{11mu} N\; i})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({2\mspace{11mu} N\; i})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({2\mspace{11mu} N\; i})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({2\mspace{11mu} N\; i})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {2\;{Ni}} \right)} \\{s\; 2\left( {2\;{Ni}} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 133}\end{matrix}$

Here, j is an imaginary unit.

For symbol number 2Ni+1:

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 127}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + 1} \right)} \\{r\; 2\left( {{2\;{Ni}} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\mspace{11mu} N\; i} + 1})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\mspace{11mu} N\; i} + 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2\mspace{11mu} N\; i} + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\mspace{11mu} N\; i} + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + 1} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 134}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 128}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + k} \right)} \\{r\; 2\left( {{2\;{Ni}} + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\mspace{11mu} N\; i} + k})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\mspace{11mu} N\; i} + k})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2\mspace{11mu} N\; i} + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\mspace{11mu} N\; i} + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + k} \right)} \\{s\; 2\left( {{2\;{Ni}} + k} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 135}\end{matrix}$

Furthermore, for symbol number 2Ni+N−1:

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 129}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + N - 1} \right)} \\{r\; 2\left( {{2\;{Ni}} + N - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\beta^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\mspace{11mu} N\; i} + N - 1})}}} & {\beta \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\mspace{11mu} N\; i} + N - 1})}} + \lambda})}}} \\{\beta \times {\mathbb{e}}^{{j\theta}_{21}{({{2\mspace{11mu} N\; i} + N - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\mspace{11mu} N\; i} + N - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N - 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + N - 1} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 136}\end{matrix}$For symbol number 2Ni+N (where i is an integer greater than or equal tozero):

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 130}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + N} \right)} \\{r\; 2\left( {{2\;{Ni}} + N} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\mspace{11mu} N\; i} + N})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\mspace{11mu} N\; i} + N})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\mspace{11mu} N\; i} + N})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\mspace{11mu} N\; i} + N})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N} \right)} \\{s\; 2\left( {{2\;{Ni}} + N} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 137}\end{matrix}$

Here, j is an imaginary unit.

For symbol number 2Ni+N+1:

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 131}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + N + 1} \right)} \\{r\; 2\left( {{2\;{Ni}} + N + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\mspace{11mu} N\; i} + N + 1})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\mspace{11mu} N\; i} + N + 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\mspace{11mu} N\; i} + N + 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\mspace{11mu} N\; i} + N + 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N + 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + N + 1} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 138}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+N+k (k=0, 1, . . . , N−1):

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 132}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + N + k} \right)} \\{r\; 2\left( {{2\;{Ni}} + N + k} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\mspace{11mu} N\; i} + N + k})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\mspace{11mu} N\; i} + N + k})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\mspace{11mu} N\; i} + N + k})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\mspace{11mu} N\; i} + N + k})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + N + k} \right)} \\{s\; 2\left( {{2\;{Ni}} + N + k} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 139}\end{matrix}$

Furthermore, for symbol number 2Ni+2N−1:

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 133}} & \; \\{\begin{pmatrix}{r\; 1\left( {{2\;{Ni}} + {2\; N} - 1} \right)} \\{r\; 2\left( {{2\;{Ni}} + {2\; N} - 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({{2\mspace{11mu} N\; i} + {2\; N} - 1})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({{2\mspace{11mu} N\; i} + {2\; N} - 1})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{2\mspace{11mu} N\; i} + {2\; N} - 1})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({{2\mspace{11mu} N\; i} + {2\; N} - 1})}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{2\;{Ni}} + {2\; N} - 1} \right)} \\{s\; 2\left( {{2\;{Ni}} + {2\; N} - 1} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 140}\end{matrix}$

As a result, when q is represented as follows, one of the signals s1 ands2 can no longer be obtained.

For symbol number 2Ni (where i is an integer greater than or equal tozero):

$\begin{matrix}{{Equation}\mspace{14mu} 134} & \; \\{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({2\mspace{11mu} N\; i})}} - {\theta_{21}{({2\mspace{11mu} N\; i})}}})}}}},{{- A}\;\beta\;{\mathbb{e}}^{j{({{\theta_{11}{({2\mspace{11mu} N\; i})}} - {\theta_{21}{({2\mspace{11mu} N\; i})}} - \delta})}}}} & {{Math}\mspace{14mu} 141}\end{matrix}$For symbol number 2Ni+1:

$\begin{matrix}{{Math}\mspace{14mu} 142} & \; \\{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + 1})}} - {\theta_{21}{({{2\;{Ni}} - 1})}}})}}}},{{- A}\;{\beta\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + 1})}} - {\theta_{21}{({{2\;{Ni}} + 1})}} - \delta})}}}} & {{Equation}\mspace{14mu} 135}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+k (k=0, 1, . . . , N−1):

$\begin{matrix}{{Math}\mspace{14mu} 143} & \; \\{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + k})}} - {\theta_{21}{({{2\;{Ni}} + k})}}})}}}},{{- A}\;{\beta\mathbb{e}}^{j{({{\theta_{11}{({{2\;{Ni}} + k})}} - {\theta_{21}{({{2\;{Ni}} + k})}} - \delta})}}}} & {{Equation}\mspace{14mu} 136}\end{matrix}$

Furthermore, for symbol number 2Ni+N−1:

$\begin{matrix}{{Equation}\mspace{14mu} 144} & \; \\{{q = {{- \frac{A}{\beta}}{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N - 1})}} - {\theta_{21}{({{2{Ni}} + N - 1})}}})}}}},{{- A}\;{\beta\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N - 1})}} - {\theta_{21}{({{2{Ni}} + N - 1})}} - \delta})}}}} & {{Math}\mspace{14mu} 137}\end{matrix}$For symbol number 2Ni+N (where i is an integer greater than or equal tozero):

$\begin{matrix}{{Equation}\mspace{14mu} 138} & \; \\{{q = {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N})}} - {\theta_{21}{({{2{Ni}} + N})}}})}}}},{{- A}\;{\alpha\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N})}} - {\theta_{21}{({{2{Ni}} + N})}} - \delta})}}}} & {{Math}\mspace{14mu} 145}\end{matrix}$For symbol number 2Ni+N+1:

$\begin{matrix}{{Equation}\mspace{14mu} 139} & \; \\{{q = {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + 1})}} - {\theta_{21}{({{2{Ni}} + N + 1})}}})}}}},{{- A}\;{\alpha\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + 1})}} - {\theta_{21}{({{2{Ni}} + N + 1})}} - \delta})}}}} & {{Math}\mspace{14mu} 146}\end{matrix}$

When generalized, this equation is as follows.

For symbol number 2Ni+N+k (k=0, 1, . . . , N−1):

$\begin{matrix}{{Equation}\mspace{14mu} 140} & \; \\{{q = {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + k})}} - {\theta_{21}{({{2{Ni}} + N + k})}}})}}}},{{- A}\;{\alpha\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + N + k})}} - {\theta_{21}{({{2{Ni}} + N + k})}} - \delta})}}}} & {{Math}\mspace{14mu} 147}\end{matrix}$

Furthermore, for symbol number 2Ni+2N−1:

$\begin{matrix}{{Equation}\mspace{14mu} 141} & \; \\{{q = {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + {2N} - 1})}} - {\theta_{21}{({{2{Ni}} + {2N} - 1})}}})}}}},{{- A}\;{\alpha\mathbb{e}}^{j{({{\theta_{11}{({{2{Ni}} + {2N} - 1})}} - {\theta_{21}{({{2{Ni}} + {2N} - 1})}} - \delta})}}}} & {{Math}\mspace{14mu} 148}\end{matrix}$

In this case, if q has the same solution in symbol numbers 2Ni through2Ni+N−1, then since the channel elements of the direct waves do notgreatly fluctuate, excellent reception quality can no longer be obtainedfor any of the symbol numbers. Therefore, it is difficult to achieve theability to correct errors, even if error correction codes areintroduced. Accordingly, for q not to have the same solution, Condition#7 or Condition #8 becomes necessary from Equations 134-141 and from thefact that α≠β when focusing on one of two solutions of q which does notinclude δ.Math 149e ^(j(θ) ¹¹ ^((2Ni+x)−θ) ²¹ ^((2Ni+x))) ≠e ^(j(θ) ¹¹ ^((2Ni+y)−θ) ²¹^((2Ni+y))) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #4(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)ande ^(j(θ) ¹¹ ^((2Ni+N+x)−θ) ²¹ ^((2Ni+N+x))) ≠e ^(j(θ) ¹¹ ^((2Ni+N+y)−θ)²¹ ^((2Ni+N+y))) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #7(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 150e ^(j(θ) ¹¹ ^((2Ni+x)−θ) ²¹ ^((2Ni+x))) ≠e ^(j(θ) ¹¹ ^((2Ni+y)−θ) ²¹^((2Ni+y))) for ∀x,∀y(x≠y;x,y=0,1,2, . . . ,2N−2,2N−1)  Condition #8

In this case, Condition #8 is similar to the conditions described inEmbodiment 1 through Embodiment 3. However, with regards to Condition#7, since α≠β, the solution not including δ among the two solutions of qis a different solution.

Next, design requirements for not only θ₁₁ and θ₁₂, but also for λ and δare described. It suffices to set λ to a certain value; it is thennecessary to establish requirements for δ. The following describes thedesign method for δ when λ is set to zero radians.

In this case, similar to the method of changing the precoding weights ina four-slot period (cycle), by defining δ so that π/2 radians≦|δ|≦πradians, excellent reception quality is achieved, particularly in an LOSenvironment.

In symbol numbers 2Ni through 2Ni+2N−1, two points q exist wherereception quality becomes poor, and therefore 4N such points exist. Inan LOS environment, in order to achieve excellent characteristics, these4N points should each have a different solution. In this case, focusingon amplitude, the following condition is necessary for Condition #7 orCondition #8, since α≠β.

$\begin{matrix}{{Condition}\mspace{14mu}{\# 9}} & \; \\{\alpha \neq \frac{1}{\beta}} & {{Math}\mspace{14mu} 151}\end{matrix}$

As described above, when a transmission device transmits a plurality ofmodulated signals from a plurality of antennas in a MIMO system, theadvantageous effect of improved transmission quality, as compared toconventional spatial multiplexing MIMO, is achieved in an LOSenvironment in which direct waves dominate by hopping between precodingweights regularly over time.

In the present embodiment, the structure of the reception device is asdescribed in Embodiment 1, and in particular with regards to thestructure of the reception device, operations have been described for alimited number of antennas, but the present invention may be embodied inthe same way even if the number of antennas increases. In other words,the number of antennas in the reception device does not affect theoperations or advantageous effects of the present embodiment.Furthermore, in the present embodiment, similar to Embodiment 1, theerror correction codes are not limited.

In the present embodiment, in contrast with Embodiment 1, the method ofchanging the precoding weights in the time domain has been described. Asdescribed in Embodiment 1, however, the present invention may besimilarly embodied by changing the precoding weights by using amulti-carrier transmission method and arranging symbols in the frequencydomain and the frequency-time domain. Furthermore, in the presentembodiment, symbols other than data symbols, such as pilot symbols(preamble, unique word, and the like), symbols for control information,and the like, may be arranged in the frame in any way.

Embodiment 5

In Embodiment 1 through Embodiment 4, the method of regularly hoppingbetween precoding weights has been described. In the present embodiment,a modification of this method is described.

In Embodiment 1 through Embodiment 4, the method of regularly hoppingbetween precoding weights as in FIG. 6 has been described. In thepresent embodiment, a method of regularly hopping between precodingweights that differs from FIG. 6 is described.

As in FIG. 6, this method hops between four different precoding weights(matrices). FIG. 22 shows the hopping method that differs from FIG. 6.In FIG. 22, four different precoding weights (matrices) are representedas W1, W2, W3, and W4. (For example, W1 is the precoding weight (matrix)in Equation 37, W2 is the precoding weight (matrix) in Equation 38, W3is the precoding weight (matrix) in Equation 39, and W4 is the precodingweight (matrix) in Equation 40.) In FIG. 3, elements that operate in asimilar way to FIG. 3 and FIG. 6 bear the same reference signs.

The parts unique to FIG. 22 are as follows.

The first period (cycle) 2201, the second period (cycle) 2202, the thirdperiod (cycle) 2203, . . . are all four-slot periods (cycles).

A different precoding weight matrix is used in each of the four slots,i.e. W1, W2, W3, and W4 are each used once.

It is not necessary for W1, W2, W3, and W4 to be in the same order inthe first period (cycle) 2201, the second period (cycle) 2202, the thirdperiod (cycle) 2203, . . . .

In order to implement this method, a precoding weight generating unit2200 receives, as an input, a signal regarding a weighting method andoutputs information 2210 regarding precoding weights in order for eachperiod (cycle). The weighting unit 600 receives, as inputs, thisinformation, s1(t), and s2(t), performs weighting, and outputs z1(t) andz2(t).

FIG. 23 shows a different weighting method than FIG. 22 for the aboveprecoding method. In FIG. 23, the difference from FIG. 22 is that asimilar method to FIG. 22 is achieved by providing a reordering unitafter the weighting unit and by reordering signals.

In FIG. 23, the precoding weight generating unit 2200 receives, as aninput, information 315 regarding a weighting method and outputsinformation 2210 on precoding weights in the order of precoding weightsW1, W2, W3, W4, W1, W2, W3, W4, . . . . Accordingly, the weighting unit600 uses the precoding weights in the order of precoding weights W1, W2,W3, W4, W1, W2, W3, W4, . . . and outputs precoded signals 2300A and2300B.

A reordering unit 2300 receives, as inputs, the precoded signals 2300Aand 2300B, reorders the precoded signals 2300A and 2300B in the order ofthe first period (cycle) 2201, the second period (cycle) 2202, and thethird period (cycle) 2203 in FIG. 23, and outputs z1(t) and z2(t).

Note that in the above description, the period (cycle) for hoppingbetween precoding weights has been described as having four slots forthe sake of comparison with FIG. 6. As in Embodiment 1 throughEmbodiment 4, however, the present invention may be similarly embodiedwith a period (cycle) having other than four slots.

Furthermore, in Embodiment 1 through Embodiment 4, and in the aboveprecoding method, within the period (cycle), the value of δ and β hasbeen described as being the same for each slot, but the value of δ and βmay change in each slot.

As described above, when a transmission device transmits a plurality ofmodulated signals from a plurality of antennas in a MIMO system, theadvantageous effect of improved transmission quality, as compared toconventional spatial multiplexing MIMO, is achieved in an LOSenvironment in which direct waves dominate by hopping between precodingweights regularly over time.

In the present embodiment, the structure of the reception device is asdescribed in Embodiment 1, and in particular with regards to thestructure of the reception device, operations have been described for alimited number of antennas, but the present invention may be embodied inthe same way even if the number of antennas increases. In other words,the number of antennas in the reception device does not affect theoperations or advantageous effects of the present embodiment.Furthermore, in the present embodiment, similar to Embodiment 1, theerror correction codes are not limited.

In the present embodiment, in contrast with Embodiment 1, the method ofchanging the precoding weights in the time domain has been described. Asdescribed in Embodiment 1, however, the present invention may besimilarly embodied by changing the precoding weights by using amulti-carrier transmission method and arranging symbols in the frequencydomain and the frequency-time domain. Furthermore, in the presentembodiment, symbols other than data symbols, such as pilot symbols(preamble, unique word, and the like), symbols for control information,and the like, may be arranged in the frame in any way.

Embodiment 6

In Embodiments 1-4, a method for regularly hopping between precodingweights has been described. In the present embodiment, a method forregularly hopping between precoding weights is again described,including the content that has been described in Embodiments 1-4.

First, out of consideration of an LOS environment, a method of designinga precoding matrix is described for a 2×2 spatial multiplexing MIMOsystem that adopts precoding in which feedback from a communicationpartner is not available.

FIG. 30 shows a model of a 2×2 spatial multiplexing MIMO system thatadopts precoding in which feedback from a communication partner is notavailable. An information vector z is encoded and interleaved. As outputof the interleaving, an encoded bit vector u(p)=(u₁(p), u₂(p)) isacquired (where p is the slot time). Let u_(i)(p)=(u_(i1)(P), . . . ,u_(i2)(p)) (where h is the number of transmission bits per symbol).Letting a signal after modulation (mapping) be s(p)=(s1(p), s2(p))^(T)and a precoding matrix be F(p), a precoded symbol x(p)=(x₁(p),x₂(p))^(T) is represented by the following equation.

$\begin{matrix}{{Equation}\mspace{14mu} 142} & \; \\\begin{matrix}{{x(p)} = \left( {{x_{1}(p)},{x_{2}(p)}} \right)^{T}} \\{= {{F(p)}{s(p)}}}\end{matrix} & {{Math}\mspace{14mu} 152}\end{matrix}$

Accordingly, letting a received vector be y(p)=(y₁(p), y₂(p))^(T), thereceived vector y(p) is represented by the following equation.

$\begin{matrix}{{Equation}\mspace{14mu} 143} & \; \\\begin{matrix}{{y(p)} = \left( {{y_{1}(p)},{y_{2}(p)}} \right)^{T}} \\{= {{{H(p)}{F(p)}{s(p)}} + {n(p)}}}\end{matrix} & {{Math}\mspace{14mu} 153}\end{matrix}$

In this Equation, H(p) is the channel matrix, n(p)=(n₁(p), n₂(p))^(T) isthe noise vector, and n_(i)(p) is the i.i.d. complex Gaussian randomnoise with an average value 0 and variance σ². Letting the Rician factorbe K, the above equation can be represented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 144} & \; \\\begin{matrix}{{y(p)} = \left( {{y_{1}(p)},{y_{2}(p)}} \right)^{T}} \\{= {{\left( {{\sqrt{\frac{K}{K + 1}}{H_{d}(p)}} + {\sqrt{\frac{1}{K + 1}}{H_{s}(p)}}} \right){F(p)}{s(p)}} + {n(p)}}}\end{matrix} & {{Math}\mspace{14mu} 154}\end{matrix}$

In this equation, H_(d)(p) is the channel matrix for the direct wavecomponents, and H_(s)(p) is the channel matrix for the scattered wavecomponents. Accordingly, the channel matrix H(p) is represented asfollows.

$\begin{matrix}{{Equation}\mspace{14mu} 145} & \; \\\begin{matrix}{{H(p)} = {{\sqrt{\frac{K}{K + 1}}{H_{d}(p)}} + {\sqrt{\frac{1}{K + 1}}{H_{s}(p)}}}} \\{= {{\sqrt{\frac{K}{K + 1}}\begin{pmatrix}h_{11,d} & h_{12,d} \\h_{21,d} & h_{22,d}\end{pmatrix}} +}} \\{\sqrt{\frac{1}{K + 1}}\begin{pmatrix}{h_{11,s}(p)} & {h_{12,s}(p)} \\{h_{21,s}(p)} & {h_{22,s}(p)}\end{pmatrix}}\end{matrix} & {{Math}\mspace{14mu} 155}\end{matrix}$

In Equation 145, it is assumed that the direct wave environment isuniquely determined by the positional relationship between transmitters,and that the channel matrix H_(d)(p) for the direct wave components doesnot fluctuate with time. Furthermore, in the channel matrix H_(d)(p) forthe direct wave components, it is assumed that as compared to theinterval between transmitting antennas, the probability of anenvironment with a sufficiently long distance between transmission andreception devices is high, and therefore that the channel matrix for thedirect wave components can be treated as a non-singular matrix.Accordingly, the channel matrix H_(d)(p) is represented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 146} & \; \\\begin{matrix}{{H_{d}(p)} = \begin{pmatrix}h_{11,d} & h_{12,d} \\h_{21,d} & h_{22,d}\end{pmatrix}} \\{= \begin{pmatrix}{A\;{\mathbb{e}}^{j\psi}} & q \\{A\;{\mathbb{e}}^{j\psi}} & q\end{pmatrix}}\end{matrix} & {{Math}\mspace{14mu} 156}\end{matrix}$

In this equation, let A be a positive real number and q be a complexnumber. Subsequently, out of consideration of an LOS environment, amethod of designing a precoding matrix is described for a 2×2 spatialmultiplexing MIMO system that adopts precoding in which feedback from acommunication partner is not available.

From Equations 144 and 145, it is difficult to seek a precoding matrixwithout appropriate feedback in conditions including scattered waves,since it is difficult to perform analysis under conditions includingscattered waves. Additionally, in a NLOS environment, little degradationin reception quality of data occurs as compared to an LOS environment.Therefore, the following describes a method of designing precodingmatrices without appropriate feedback in an LOS environment (precodingmatrices for a precoding method that hops between precoding matricesover time).

As described above, since it is difficult to perform analysis underconditions including scattered waves, an appropriate precoding matrixfor a channel matrix including components of only direct waves is soughtfrom Equations 144 and 145. Therefore, in Equation 144, the case whenthe channel matrix includes components of only direct waves isconsidered. It follows that from Equation 146, Equation 144 can berepresented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 147} & \; \\\begin{matrix}{\begin{pmatrix}{y_{1}(p)} \\{y_{2}(p)}\end{pmatrix} = {{{H_{d}(p)}{F(p)}{s(p)}} + {n(p)}}} \\{= {{\begin{pmatrix}{A\;{\mathbb{e}}^{j\psi}} & q \\{A\;{\mathbb{e}}^{j\psi}} & q\end{pmatrix}{F(p)}{s(p)}} + {n(p)}}}\end{matrix} & {{Math}\mspace{14mu} 157}\end{matrix}$

In this equation, a unitary matrix is used as the precoding matrix.Accordingly, the precoding matrix is represented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 148} & \; \\{{F(p)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \pi})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 158}\end{matrix}$

In this equation, λ is a fixed value. Therefore, Equation 147 can berepresented as follows.

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 149}} & \; \\{\begin{pmatrix}{y_{1}(p)} \\{y_{2}(p)}\end{pmatrix} = {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\psi}} & q \\{A\;{\mathbb{e}}^{j\psi}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \pi})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {n(p)}}} & {{Math}\mspace{14mu} 159}\end{matrix}$

As is clear from Equation 149, when the reception device performs linearoperation of Zero Forcing (ZF) or the Minimum Mean Squared Error (MMSE),the transmitted bit cannot be determined by s1(p), s2(p). Therefore, theiterative APP (or iterative Max-log APP) or APP (or Max-log APP)described in Embodiment 1 is performed (hereafter referred to as MaximumLikelihood (ML) calculation), the log-likelihood ratio of each bittransmitted in s1(p), s2(p) is sought, and decoding with errorcorrection codes is performed. Accordingly, the following describes amethod of designing a precoding matrix without appropriate feedback inan LOS environment for a reception device that performs ML calculation.

The precoding in Equation 149 is considered. The right-hand side andleft-hand side of the first line are multiplied by e^(−jΨ), andsimilarly the right-hand side and left-hand side of the second line aremultiplied by e^(−jΨ). The following equation represents the result.

$\begin{matrix}{{Equation}\mspace{14mu} 150} & \; \\{\begin{pmatrix}{{\mathbb{e}}^{- {j\psi}}{y_{1}(p)}} \\{{\mathbb{e}}^{- {j\psi}}{y_{2}(p)}}\end{pmatrix} = {{{\mathbb{e}}^{- {j\psi}}\left\{ {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\psi}} & q \\{A\;{\mathbb{e}}^{j\psi}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \pi})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {n(p)}} \right\}} = {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j0}} & {{\mathbb{e}}^{- {j\psi}}q} \\{A\;{\mathbb{e}}^{j0}} & {{\mathbb{e}}^{- {j\psi}}q}\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \pi})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {{\mathbb{e}}^{- {j\psi}}{n(p)}}}}} & {{Math}\mspace{14mu} 160}\end{matrix}$

e^(−jΨ)y₁(p), e^(−jΨ)y₂(p), and e^(−jΨ)q are respectively redefined asy₁(p), y₂(p), and q. Furthermore, since e^(−jΨ)n(p)=e^(−jΨ)n₁(p),e^(−jΨ)n₂(p))^(T), and e^(−jΨ)n₁(p), e^(−jΨ)n₂(p) are the independentidentically distributed (i.i.d.) complex Gaussian random noise with anaverage value 0 and variance σ², e^(−jΨ)n(p) is redefined as n(p). As aresult, generality is not lost by restating Equation 150 as Equation151.

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 161}} & \; \\{\begin{pmatrix}{y_{1}(p)} \\{y_{2}(p)}\end{pmatrix} = {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\; e^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{(p)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \pi})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {n(p)}}} & {{Equation}\mspace{14mu} 151}\end{matrix}$

Next, Equation 151 is transformed into Equation 152 for the sake ofclarity.

$\begin{matrix}{\mspace{85mu}{{Math}\mspace{14mu} 162}} & \; \\{\begin{pmatrix}{y_{1}(p)} \\{y_{2}(p)}\end{pmatrix} = {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \pi})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {n(p)}}} & {{Equation}\mspace{14mu} 152}\end{matrix}$

In this case, letting the minimum Euclidian distance between a receivedsignal point and a received candidate signal point be d_(min) ², then apoor point has a minimum value of zero for d_(min) ², and two values ofq exist at which conditions are poor in that all of the bits transmittedby s1(p) and all of the bits transmitted by s2(p) being eliminated.

In Equation 152, when s1(p) does not exist.

$\begin{matrix}{{Math}\mspace{14mu} 163} & \; \\{q = {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{(p)}} - {\theta_{21}{(p)}}})}}}} & {{Equation}\mspace{14mu} 153}\end{matrix}$

In Equation 152, when s2(p) does not exist.Math 164q=−Aα _(e) ^(j(θ) ¹¹ ^((p)−θ) ²¹ ^((p)−π))  Equation 154

(Hereinafter, the values of q satisfying Equations 153 and 154 arerespectively referred to as “poor reception points for s1 and s2”).

When Equation 153 is satisfied, since all of the bits transmitted bys1(p) are eliminated, the received log-likelihood ratio cannot be soughtfor any of the bits transmitted by s1(p). When Equation 154 issatisfied, since all of the bits transmitted by s2(p) are eliminated,the received log-likelihood ratio cannot be sought for any of the bitstransmitted by s2(p).

A broadcast/multicast transmission system that does not change theprecoding matrix is now considered. In this case, a system model isconsidered in which a base station transmits modulated signals using aprecoding method that does not hop between precoding matrices, and aplurality of terminals (Γ terminals) receive the modulated signalstransmitted by the base station.

It is considered that the conditions of direct waves between the basestation and the terminals change little over time. Therefore, fromEquations 153 and 154, for a terminal that is in a position fitting theconditions of Equation 155 or Equation 156 and that is in an LOSenvironment where the Rician factor is large, the possibility ofdegradation in the reception quality of data exists. Accordingly, toresolve this problem, it is necessary to change the precoding matrixover time.

$\begin{matrix}{{Math}\mspace{14mu} 165} & \; \\{q \approx {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{(p)}} - {\theta_{21}{(p)}}})}}}} & {{Equation}\mspace{14mu} 155}\end{matrix}$Math 166q≈−Aα _(e) ^(j(θ) ¹¹ ^((p)−θ) ²¹ ^((p)−π))  Equation 156

A method of regularly hopping between precoding matrices over a timeperiod (cycle) with N slots (hereinafter referred to as a precodinghopping method) is considered.

Since there are N slots in the time period (cycle), N varieties ofprecoding matrices F[i] based on Equation 148 are prepared (i=0, 1, . .. , N−1). In this case, the precoding matrices F[i] are represented asfollows.

$\begin{matrix}{{Math}\mspace{14mu} 167} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{\lbrack{\mathbb{i}}\rbrack}}} & {\mathbb{e}}^{j{({{\theta_{21}{\lbrack{\mathbb{i}}\rbrack}} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 157}\end{matrix}$

In this equation, let α not change over time, and let λ also not changeover time (though change over time may be allowed).

As in Embodiment 1, F[i] is the precoding matrix used to obtain aprecoded signal x (p=N×k+i) in Equation 142 for time N×k+i (where k isan integer equal to or greater than 0, and i=0, 1, . . . , N−1). Thesame is true below as well.

At this point, based on Equations 153 and 154, design conditions such asthe following are important for the precoding matrices for precodinghopping.

Condition #10Math 168e ^(j(θ) ¹¹ ^([x]−θ) ²¹ ^([x]−π)) ≠e ^(j(θ) ¹¹ ^([y]−θ) ²¹^([y]))  Equation 158for ∀x, ∀y (x≠y; x,y=0,1, . . . , N−1)Condition #11Math 169e ^(j(θ) ¹¹ ^([x]−θ) ²¹ ^([x]−π)) ≠e ^(j(θ) ¹¹ ^([y]−θ) ²¹^([y]−π))  Equation 159for ∀x, ∀y (x≠y; x,y=0,1, . . . , N−1)

From Condition #10, in all of the Γ terminals, there is one slot or lesshaving poor reception points for s1 among the N slots in a time period(cycle). Accordingly, the log-likelihood ratio for bits transmitted bys1(p) can be obtained for at least N−1 slots. Similarly, from Condition#11, in all of the Γ terminals, there is one slot or less having poorreception points for s2 among the N slots in a time period (cycle).Accordingly, the log-likelihood ratio for bits transmitted by s2(p) canbe obtained for at least N−1 slots.

In this way, by providing the precoding matrix design model of Condition#10 and Condition #11, the number of bits for which the log-likelihoodratio is obtained among the bits transmitted by s1(p), and the number ofbits for which the log-likelihood ratio is obtained among the bitstransmitted by s2(p) is guaranteed to be equal to or greater than afixed number in all of the Γ terminals. Therefore, in all of the Γterminals, it is considered that degradation of data reception qualityis moderated in an LOS environment where the Rician factor is large.

The following shows an example of a precoding matrix in the precodinghopping method.

The probability density distribution of the phase of a direct wave canbe considered to be evenly distributed over [0 2π]. Therefore, theprobability density distribution of the phase of q in Equations 151 and152 can also be considered to be evenly distributed over [0 2π].Accordingly, the following is established as a condition for providingfair data reception quality insofar as possible for Γ terminals in thesame LOS environment in which only the phase of q differs.

Condition #12

When using a precoding hopping method with an N-slot time period(cycle), among the N slots in the time period (cycle), the poorreception points for s1 are arranged to have an even distribution interms of phase, and the poor reception points for s2 are arranged tohave an even distribution in terms of phase.

The following describes an example of a precoding matrix in theprecoding hopping method based on Condition #10 through Condition #12.Let α=1.0 in the precoding matrix in Equation 157.

Example #5

Let the number of slots N in the time period (cycle) be 8. In order tosatisfy Condition #10 through Condition #12, precoding matrices for aprecoding hopping method with an N=8 time period (cycle) are provided asin the following equation.

$\begin{matrix}{{Math}\mspace{14mu} 170} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 160}\end{matrix}$

Here, j is an imaginary unit, and i=0, 1, . . . , 7. Instead of Equation160, Equation 161 may be provided (where λ and θ₁₁[i] do not change overtime (though change may be allowed)).

$\begin{matrix}{{Math}\mspace{14mu} 171} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 161}\end{matrix}$

Accordingly, the poor reception points for s1 and s2 become as in FIGS.31A and 31B. (In FIGS. 31A and 31B, the horizontal axis is the realaxis, and the vertical axis is the imaginary axis.) Instead of Equations160 and 161, Equations 162 and 163 may be provided (where i=0, 1, . . ., 7, and where λ and θ₁₁[i] do not change over time (though change maybe allowed)).

$\begin{matrix}{{Math}\mspace{14mu} 172} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j{({- \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 162} \\{{Math}\mspace{14mu} 173} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 163}\end{matrix}$

Next, the following is established as a condition, different fromCondition #12, for providing fair data reception quality insofar aspossible for Γ terminals in the same LOS environment in which only thephase of q differs.

Condition #13

When using a precoding hopping method with an N-slot time period(cycle), in addition to the conditionMath 174e ^(j(θ) ¹¹ ^([x]−θ) ²¹ ^([x])) ≠e ^(j(θ) ¹¹ ^([y]−θ) ²¹ ^([y]−π)) for∀x,∀y(x,y=0,1, . . . , N−1  Equation 164the poor reception points for s1 and the poor reception points for s2are arranged to be in an even distribution with respect to phase in theN slots in the time period (cycle).

The following describes an example of a precoding matrix in theprecoding hopping method based on Condition #10, Condition #11, andCondition #13. Let α=1.0 in the precoding matrix in Equation 157.

Example #6

Let the number of slots N in the time period (cycle) be 4. Precodingmatrices for a precoding hopping method with an N=4 time period (cycle)are provided as in the following equation.

$\begin{matrix}{{Math}\mspace{14mu} 175} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\frac{{\mathbb{i}}\;\pi}{4}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 165}\end{matrix}$

Here, j is an imaginary unit, and i=0, 1, 2, 3. Instead of Equation 165,Equation 166 may be provided (where λ and θ₁₁ [i] do not change overtime (though change may be allowed)).

$\begin{matrix}{{Math}\mspace{14mu} 176} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 166}\end{matrix}$

Accordingly, the poor reception points for s1 and s2 become as in FIG.32. (In FIG. 32, the horizontal axis is the real axis, and the verticalaxis is the imaginary axis.) Instead of Equations 165 and 166, Equations167 and 168 may be provided (where i=0, 1, 2, 3, and where λ and θ₁₁[i]do not change over time (though change may be allowed)).

$\begin{matrix}{{Math}\mspace{14mu} 177} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j{({- \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{- \frac{{\mathbb{i}}\;\pi}{4}} + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 167} \\{{Math}\mspace{14mu} 178} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda + \pi})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 168}\end{matrix}$

Next, a precoding hopping method using a non-unitary matrix isdescribed.

Based on Equation 148, the precoding matrices presently underconsideration are represented as follows.

$\begin{matrix}{{Math}\mspace{14mu} 179} & \; \\{{F(p)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 169}\end{matrix}$

Equations corresponding to Equations 151 and 152 are represented asfollows.

$\begin{matrix}{\mspace{79mu}{{Math}\mspace{14mu} 180}} & \; \\{\begin{pmatrix}{y_{1}(p)} \\{y_{2}(p)}\end{pmatrix} = {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q \\{A\; e^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{(p)}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {n(p)}}} & {{Equation}\mspace{14mu} 170} \\{\mspace{79mu}{{Math}\mspace{14mu} 181}} & \; \\{\begin{pmatrix}{y_{1}(p)} \\{y_{2}(p)}\end{pmatrix} = {{\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{A\;{\mathbb{e}}^{j\; 0}} & q\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(p)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{(p)}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{(p)}}} & {\mathbb{e}}^{j{({{\theta_{21}{(p)}} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1(p)} \\{s\; 2(p)}\end{pmatrix}} + {n(p)}}} & {{Equation}\mspace{14mu} 171}\end{matrix}$

In this case, there are two q at which the minimum value d_(min) ² ofthe Euclidian distance between a received signal point and a receivedcandidate signal point is zero.

In Equation 171, when s1(p) does not exist:

$\begin{matrix}{{Math}\mspace{14mu} 182} & \; \\{q = {{- \frac{A}{\alpha}}{\mathbb{e}}^{j{({{\theta_{11}{(p)}} - {\theta_{21}{(p)}}})}}}} & {{Equation}\mspace{14mu} 172}\end{matrix}$

In Equation 171, when s2(p) does not exist:Math 183q=−Aα _(e) ^(j(θ) ¹¹ ^((p)−θ) ²¹ ^((p)−δ))  Equation 173

In the precoding hopping method for an N-slot time period (cycle), byreferring to Equation 169, N varieties of the precoding matrix F[i] arerepresented as follows.

$\begin{matrix}{{Math}\mspace{14mu} 184} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{\lbrack{\mathbb{i}}\rbrack}}} & {\mathbb{e}}^{j{({{\theta_{21}{\lbrack{\mathbb{i}}\rbrack}} + \lambda + \delta})}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 174}\end{matrix}$

In this equation, let α and δ not change over time. At this point, basedon Equations 34 and 35, design conditions such as the following areprovided for the precoding matrices for precoding hopping.

Condition #14Math 185e ^(j(θ) ¹¹ ^([x]−θ) ²¹ ^([x])) ≠e ^(j(θ) ¹¹ ^([y]−θ) ²¹ ^([y])) for∀x,•y(x≠y;x,y=0,1, . . . , N−1)  Equation 175Condition #15Math 186e ^(j(θ) ¹¹ ^([x]−θ) ²¹ ^([x]−δ)) ≠e ^(j(θ) ¹¹ ^([y]−θ) ²¹ ^([y]−δ)) for∀x,•y(x≠y;x,y=0,1, . . . ,N−1)  Equation 176

Example #7

Let α=1.0 in the precoding matrix in Equation 174. Let the number ofslots N in the time period (cycle) be 16. In order to satisfy Condition#12, Condition #14, and Condition #15, precoding matrices for aprecoding hopping method with an N=16 time period (cycle) are providedas in the following equations.

For i=0, 1, . . . , 7:

$\begin{matrix}{{Equation}\mspace{14mu} 177} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0} \\{\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}} & {\mathbb{e}}^{j{({\frac{\mathbb{i}\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 187}\end{matrix}$For i=8, 9, . . . , 15:

$\begin{matrix}{{Equation}\mspace{14mu} 178} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}} & {\mathbb{e}}^{j{({\frac{\mathbb{i}\pi}{4} + \frac{7\pi}{8}})}} \\{\mathbb{e}}^{j\; 0} & {\mathbb{e}}^{j\; 0}\end{pmatrix}}} & {{Math}\mspace{14mu} 188}\end{matrix}$

Furthermore, a precoding matrix that differs from Equations 177 and 178can be provided as follows.

For i=0, 1, . . . , 7:

$\begin{matrix}{{Equation}\mspace{14mu} 179} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{\mathbb{i}\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{\mathbb{i}\pi}{4} + \lambda + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 189}\end{matrix}$For i=8, 9, . . . , 15:

$\begin{matrix}{{Equation}\mspace{14mu} 180} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{\mathbb{i}\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{\mathbb{i}\pi}{4} + \lambda + \frac{7\pi}{8}})}} \\{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 190}\end{matrix}$

Accordingly, the poor reception points for s1 and s2 become as in FIGS.33A and 33B.

(In FIGS. 33A and 33B, the horizontal axis is the real axis, and thevertical axis is the imaginary axis.) Instead of Equations 177 and 178,and Equations 179 and 180, precoding matrices may be provided as below.

For i=0, 1, . . . , 7:

$\begin{matrix}{{Equation}\mspace{14mu} 181} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j{({- \frac{\mathbb{i}\pi}{4}})}} & {\mathbb{e}}^{j{({{- \frac{\mathbb{i}\pi}{4}} + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 191}\end{matrix}$For i=8, 9, . . . , 15:

$\begin{matrix}{{Equation}\mspace{14mu} 182} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j{({- \frac{\mathbb{i}\pi}{4}})}} & {\mathbb{e}}^{j{({{- \frac{\mathbb{i}\pi}{4}} + \frac{7\pi}{8}})}} \\{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0}\end{pmatrix}}} & {{Math}\mspace{14mu} 192}\end{matrix}$

Or

For i=0, 1, . . . , 7:

$\begin{matrix}{{Equation}\mspace{14mu} 183} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{\mathbb{i}\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{\mathbb{i}\pi}{4} + \lambda + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 193}\end{matrix}$For i=8, 9, . . . , 15:

$\begin{matrix}{{Equation}\mspace{14mu} 184} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{\mathbb{i}\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{\mathbb{i}\pi}{4} + \lambda + \frac{7\pi}{8}})}} \\{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 194}\end{matrix}$(In Equations 177-184, 7π/8 may be changed to −7π/8.)

Next, the following is established as a condition, different fromCondition #12, for providing fair data reception quality insofar aspossible for Γ terminals in the same LOS environment in which only thephase of q differs.

Condition #16

When using a precoding hopping method with an N-slot time period(cycle), the following condition is set:Math 195e ^(j(θ) ¹¹ ^([x]−θ) ²¹ ^([x])) ≠e ^(j(θ) ¹¹ ^([y]−θ) ²¹ ^([y]−δ)) for∀x,∀y(x,y=0,1, . . . ,N−1  Equation 185

and the poor reception points for s1 and the poor reception points fors2 are arranged to be in an even distribution with respect to phase inthe N slots in the time period (cycle).

The following describes an example of a precoding matrix in theprecoding hopping method based on Condition #14, Condition #15, andCondition #16. Let α=1.0 in the precoding matrix in Equation 174.

Example #8

Let the number of slots N in the time period (cycle) be 8. Precodingmatrices for a precoding hopping method with an N=8 time period (cycle)are provided as in the following equation.

$\begin{matrix}{{Equation}\mspace{14mu} 186} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}} & {\mathbb{e}}^{j{({\frac{\mathbb{i}\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 196}\end{matrix}$

Here, i=0, 1, . . . , 7.

Furthermore, a precoding matrix that differs from Equation 186 can beprovided as follows (where i=0, 1, . . . , 7, and where λ and θ₁₁ [i] donot change over time (though change may be allowed)).

$\begin{matrix}{{Equation}\mspace{14mu} 187} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{\mathbb{i}\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{\mathbb{i}\pi}{4} + \lambda + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 197}\end{matrix}$

Accordingly, the poor reception points for s1 and s2 become as in FIG.34. Instead of Equations 186 and 187, precoding matrices may be providedas follows (where i=0, 1, . . . , 7, and where λ and θ₁₁[i] do notchange over time (though change may be allowed)).

$\begin{matrix}{{Equation}\mspace{14mu} 188} & \; \\{{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\mathbb{e}}^{j0} \\{\mathbb{e}}^{j{({- \frac{\mathbb{i}\pi}{4}})}} & {\mathbb{e}}^{j{({{- \frac{\mathbb{i}\pi}{4}} + \frac{7\pi}{8}})}}\end{pmatrix}}}{or}} & {{Math}\mspace{14mu} 198} \\{{Equation}\mspace{14mu} 189} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}} \\{\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{\mathbb{i}\pi}{4}})}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{\mathbb{i}\pi}{4} + \lambda + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 199}\end{matrix}$(In Equations 186-189, 7π/8 may be changed to −7π/8.)

Next, in the precoding matrix of Equation 174, a precoding hoppingmethod that differs from Example #7 and Example #8 by letting α≠1, andby taking into consideration the distance in the complex plane betweenpoor reception points, is examined.

In this case, the precoding hopping method for an N-slot time period(cycle) of Equation 174 is used, and from Condition #14, in all of the Γterminals, there is one slot or less having poor reception points for s1 among the N slots in a time period (cycle). Accordingly, thelog-likelihood ratio for bits transmitted by s1(p) can be obtained forat least N−1 slots. Similarly, from Condition #15, in all of the Γterminals, there is one slot or less having poor reception points for s2among the N slots in a time period (cycle). Accordingly, thelog-likelihood ratio for bits transmitted by s2(p) can be obtained forat least N−1 slots.

Therefore, it is clear that a larger value for N in the N-slot timeperiod (cycle) increases the number of slots in which the log-likelihoodratio can be obtained.

Incidentally, since the influence of scattered wave components is alsopresent in an actual channel model, it is considered that when thenumber of slots N in the time period (cycle) is fixed, there is apossibility of improved data reception quality if the minimum distancein the complex plane between poor reception points is as large aspossible. Accordingly, in the context of Example #7 and Example #8,precoding hopping methods in which α≠1 and which improve on Example #7and Example #8 are considered. The precoding method that improves onExample #8 is easier to understand and is therefore described first.

Example #9

From Equation 186, the precoding matrices in an N=8 time period (cycle)precoding hopping method that improves on Example #8 are provided in thefollowing equation.

$\begin{matrix}{{Equation}\mspace{14mu} 190} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{\mathbb{i}\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 200}\end{matrix}$

Here, i=0, 1, . . . , 7. Furthermore, precoding matrices that differfrom Equation 190 can be provided as follows (where i=0, 1, . . . , 7,and where λ and θ₁₁[i] do not change over time (though change may beallowed)).

$\begin{matrix}{{Equation}\mspace{14mu} 191} & \; \\{{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{\mathbb{i}\pi}{4} + \lambda + \frac{7\pi}{8}})}}\end{pmatrix}}}{or}} & {{Math}\mspace{14mu} 201} \\{{Equation}\mspace{14mu} 192} & \; \\{{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j{({- \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{- \frac{\mathbb{i}\pi}{4}} + \frac{7\pi}{8}})}}\end{pmatrix}}}{or}} & {{Math}\mspace{14mu} 202} \\{{Equation}\mspace{14mu} 193} & \; \\{{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{\mathbb{i}\pi}{4} + \lambda + \frac{7\pi}{8}})}}\end{pmatrix}}}{or}} & {{Math}\mspace{14mu} 203} \\{{Equation}\mspace{14mu} 194} & \; \\{{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{\mathbb{i}\pi}{4} - \frac{7\pi}{8}})}}\end{pmatrix}}}{or}} & {{Math}\mspace{14mu} 204} \\{{Equation}\mspace{14mu} 195} & \; \\{{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \frac{\mathbb{i}\pi}{4} + \lambda - \frac{7\pi}{8}})}}\end{pmatrix}}}{or}} & {{Math}\mspace{14mu} 205} \\{{Equation}\mspace{14mu} 196} & \; \\{{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j{({- \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{- \frac{\mathbb{i}\pi}{4}} - \frac{7\pi}{8}})}}\end{pmatrix}}}{or}} & {{Math}\mspace{14mu} 206} \\{{Equation}\mspace{14mu} 197} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack{\mathbb{i}}\rbrack}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{\mathbb{i}\pi}{4} + \lambda - \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 207}\end{matrix}$

Therefore, the poor reception points for s1 and s2 are represented as inFIG. 35A when α<1.0 and as in FIG. 35B when α>1.0.

(i) When α<1.0

When α<1.0, the minimum distance in the complex plane between poorreception points is represented as min{d_(#1,#2), d_(#1,#3)} whenfocusing on the distance (d_(#1,#2)) between poor reception points #1and #2 and the distance (d_(#1,#3)) between poor reception points #1 and#3. In this case, the relationship between α and d_(#1,#2) and between αand d_(#1,#3) is shown in FIG. 36. The α which makes min{d_(#1,#2),d_(#1,#3)} the largest is as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 198} & \; \\{\alpha = {\frac{1}{\sqrt{{\cos\left( \frac{\pi}{8} \right)} + {\sqrt{3}{\sin\left( \frac{\pi}{8} \right)}}}} \approx 0.7938}} & {{Math}\mspace{14mu} 208}\end{matrix}$

The min{d_(#1,#2),d#₁,#₃} in this case is as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 199} & \; \\{{\min\left\{ {d_{{\# 1},{\# 2}},d_{{\# 1},{\# 3}}} \right\}} = {\frac{2\; A\;{\sin\left( \frac{\pi}{8} \right)}}{\sqrt{{\cos\left( \frac{\pi}{8} \right)} + {\sqrt{3}{\sin\left( \frac{\pi}{8} \right)}}}} \approx {0.6076\; A}}} & {{Math}\mspace{14mu} 209}\end{matrix}$

Therefore, the precoding method using the value of a in Equation 198 forEquations 190-197 is effective. Setting the value of α as in Equation198 is one appropriate method for obtaining excellent data receptionquality. Setting α to be a value near Equation 198, however, maysimilarly allow for excellent data reception quality. Accordingly, thevalue to which α is set is not limited to Equation 198.

(ii) When α>1.0

When α>1.0, the minimum distance in the complex plane between poorreception points is represented as min {d_(#4,#5), d_(#4,#6)} whenfocusing on the distance (d_(#4,#5)) between poor reception points #4and #5 and the distance (d_(#4,#6)) between poor reception points #4 and#6. In this case, the relationship between α and d_(#4,#5) and between αand d_(#4,#6) is shown in FIG. 37. The α which makes min {d_(#4,#5),d_(#4,#6)} the largest is as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 200} & \; \\\begin{matrix}{\alpha = \sqrt{{\cos\left( \frac{\pi}{8} \right)} + {\sqrt{3}{\sin\left( \frac{\pi}{8} \right)}}}} \\{\approx 1.2596}\end{matrix} & {{Math}\mspace{14mu} 210}\end{matrix}$

The min {d_(#4,#5), d_(#4,#6)} in this case is as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 201} & \; \\\begin{matrix}{{\min\left\{ {d_{{\# 4},{\# 5}},d_{{\# 4},{\# 6}}} \right\}} = \frac{2\; A\;{\sin\left( \frac{\pi}{8} \right)}}{\sqrt{{\cos\left( \frac{\pi}{8} \right)} + {\sqrt{3}{\sin\left( \frac{\pi}{8} \right)}}}}} \\{\approx {0.6076A}}\end{matrix} & {{Math}\mspace{14mu} 211}\end{matrix}$

Therefore, the precoding method using the value of a in Equation 200 forEquations 190-197 is effective. Setting the value of α as in Equation200 is one appropriate method for obtaining excellent data receptionquality. Setting α to be a value near Equation 200, however, maysimilarly allow for excellent data reception quality. Accordingly, thevalue to which α is set is not limited to Equation 200.

Example #10

Based on consideration of Example #9, the precoding matrices in an N=16time period (cycle) precoding hopping method that improves on Example #7are provided in the following equations (where 2 and θ₁₁[i] do notchange over time (though change may be allowed)).

For i=0, 1, . . . , 7:

$\begin{matrix}{{Equation}\mspace{14mu} 202} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{\mathbb{i}\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 212}\end{matrix}$For i=8, 9, . . . , 15:

$\begin{matrix}{{Equation}\mspace{14mu} 203} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{\mathbb{i}\pi}{4} + \frac{7\pi}{8}})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Math}\mspace{14mu} 213}\end{matrix}$

Or

For i=0, 1, . . . , 7:

$\begin{matrix}{{Equation}\mspace{14mu} 204} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack i\rbrack}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{\mathbb{i}\pi}{4} + \lambda + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 214}\end{matrix}$For i=8, 9, . . . , 15:

$\begin{matrix}{{Equation}\mspace{14mu} 205} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{\mathbb{i}\pi}{4} + \lambda + \frac{7\pi}{8}})}} \\{\mathbb{e}}^{{j\theta}_{11}{\lbrack i\rbrack}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}}\end{pmatrix}}} & {{Math}\mspace{14mu} 215}\end{matrix}$

Or

For i=0, 1, . . . , 7:

$\begin{matrix}{{Equation}\mspace{14mu} 206} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j{({- \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{- \frac{\mathbb{i}\pi}{4}} + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 216}\end{matrix}$For i=8, 9, . . . , 15:

$\begin{matrix}{{Equation}\mspace{14mu} 207} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({- \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{- \frac{\mathbb{i}\pi}{4}} + \frac{7\pi}{8}})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Math}\mspace{14mu} 217}\end{matrix}$

Or

For i=0, 1, . . . , 7:

$\begin{matrix}{{Equation}\mspace{14mu} 208} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack i\rbrack}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{\mathbb{i}\pi}{4} + \lambda + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 218}\end{matrix}$For i=8, 9, . . . , 15:

$\begin{matrix}{{Equation}\mspace{14mu} 209} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} - \frac{\mathbb{i}\pi}{4} + \lambda + \frac{7\pi}{8}})}} \\{\mathbb{e}}^{{j\theta}_{11}{\lbrack i\rbrack}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}}\end{pmatrix}}} & {{Math}\mspace{14mu} 219}\end{matrix}$

Or

For i=0, 1, . . . , 7:

$\begin{matrix}{{Equation}\mspace{14mu} 210} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{\mathbb{i}\pi}{4} - \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 220}\end{matrix}$For i=8, 9, . . . , 15:

$\begin{matrix}{{Equation}\mspace{14mu} 211} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\frac{\mathbb{i}\pi}{4}}} & {\mathbb{e}}^{j{({\frac{\mathbb{i}\pi}{4} - \frac{7\pi}{8}})}} \\{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}}\end{pmatrix}}} & {{Math}\mspace{14mu} 221}\end{matrix}$

Or

For i=0, 1, . . . , 7:

$\begin{matrix}{{Equation}\mspace{14mu} 212} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{\lbrack i\rbrack}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{\mathbb{i}\pi}{4} + \lambda - \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 222}\end{matrix}$For i=8, 9, . . . , 15:

$\begin{matrix}{{Equation}\mspace{14mu} 213} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \frac{\mathbb{i}\pi}{4} + \lambda - \frac{7\pi}{8}})}} \\{\mathbb{e}}^{{j\theta}_{11}{\lbrack i\rbrack}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack i\rbrack}} + \lambda})}}}\end{pmatrix}}} & {{Math}\mspace{14mu} 223}\end{matrix}$

Or

For i=0, 1, . . . , 7:

$\begin{matrix}{{Equation}\mspace{14mu} 214} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j{({- \frac{\mathbb{i}\pi}{4}})}}} & {\mathbb{e}}^{j{({{- \frac{\mathbb{i}\pi}{4}} - \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 224}\end{matrix}$For i=8, 9, . . . , 15:

$\begin{matrix}{{Equation}\mspace{14mu} 215} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({- \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{- \frac{\mathbb{i}\pi}{4}} - \frac{7\pi}{8}})}} \\{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}}\end{pmatrix}}} & {{Math}\mspace{14mu} 225}\end{matrix}$

Or

For i=0, 1, . . . , 7:

$\begin{matrix}{{Equation}\mspace{14mu} 216} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda - \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 226}\end{matrix}$For i=8, 9, . . . , 15:

$\begin{matrix}{{Equation}\mspace{14mu} 217} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} - \frac{{\mathbb{i}}\;\pi}{4} + \lambda - \frac{7\pi}{8}})}} \\{\mathbb{e}}^{j\;{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{\lbrack{\mathbb{i}}\rbrack}} + \lambda})}}}\end{pmatrix}}} & {{Math}\mspace{14mu} 227}\end{matrix}$

The value of α in Equation 198 and in Equation 200 is appropriate forobtaining excellent data reception quality. The poor reception pointsfor s1 are represented as in FIGS. 38A and 38B when α<1.0 and as inFIGS. 39A and 39B when α>1.0.

In the present embodiment, the method of structuring N differentprecoding matrices for a precoding hopping method with an N-slot timeperiod (cycle) has been described. In this case, as the N differentprecoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] areprepared. In the present embodiment, an example of a single carriertransmission method has been described, and therefore the case ofarranging symbols in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1]in the time domain (or the frequency domain) has been described. Thepresent invention is not, however, limited in this way, and the Ndifferent precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1]generated in the present embodiment may be adapted to a multi-carriertransmission method such as an OFDM transmission method or the like. Asin Embodiment 1, as a method of adaption in this case, precoding weightsmay be changed by arranging symbols in the frequency domain and in thefrequency-time domain. Note that a precoding hopping method with anN-slot time period (cycle) has been described, but the same advantageouseffects may be obtained by randomly using N different precodingmatrices. In other words, the N different precoding matrices do notnecessarily need to be used in a regular period (cycle).

Examples #5 through #10 have been shown based on Conditions #10 through#16. However, in order to achieve a precoding matrix hopping method witha longer period (cycle), the period (cycle) for hopping betweenprecoding matrices may be lengthened by, for example, selecting aplurality of examples from Examples #5 through #10 and using theprecoding matrices indicated in the selected examples. For example, aprecoding matrix hopping method with a longer period (cycle) may beachieved by using the precoding matrices indicated in Example #7 and theprecoding matrices indicated in Example #10. In this case, Conditions#10 through #16 are not necessarily observed. (In Equation 158 ofCondition #10, Equation 159 of Condition #11, Equation 164 of Condition#13, Equation 175 of Condition #14, and Equation 176 of Condition #15,it becomes important for providing excellent reception quality for theconditions “all x and all y” to be “existing x and existing y”.) Whenviewed from a different perspective, in the precoding matrix hoppingmethod over an N-slot period (cycle) (where N is a large naturalnumber), the probability of providing excellent reception qualityincreases when the precoding matrices of one of Examples #5 through #10are included.

Embodiment 7

The present embodiment describes the structure of a reception device forreceiving modulated signals transmitted by a transmission method thatregularly hops between precoding matrices as described in Embodiments1-6.

In Embodiment 1, the following method has been described. A transmissiondevice that transmits modulated signals, using a transmission methodthat regularly hops between precoding matrices, transmits informationregarding the precoding matrices. Based on this information, a receptiondevice obtains information on the regular precoding matrix hopping usedin the transmitted frames, decodes the precoding, performs detection,obtains the log-likelihood ratio for the transmitted bits, andsubsequently performs error correction decoding.

The present embodiment describes the structure of a reception device,and a method of hopping between precoding matrices, that differ from theabove structure and method.

FIG. 40 is an example of the structure of a transmission device in thepresent embodiment. Elements that operate in a similar way to FIG. 3bear the same reference signs. An encoder group (4002) receivestransmission bits (4001) as input. The encoder group (4002), asdescribed in Embodiment 1, includes a plurality of encoders for errorcorrection coding, and based on the frame structure signal 313, acertain number of encoders operate, such as one encoder, two encoders,or four encoders.

When one encoder operates, the transmission bits (4001) are encoded toyield encoded transmission bits. The encoded transmission bits areallocated into two parts, and the encoder group (4002) outputs allocatedbits (4003A) and allocated bits (4003B).

When two encoders operate, the transmission bits (4001) are divided intwo (referred to as divided bits A and B). The first encoder receivesthe divided bits A as input, encodes the divided bits A, and outputs theencoded bits as allocated bits (4003A). The second encoder receives thedivided bits B as input, encodes the divided bits B, and outputs theencoded bits as allocated bits (4003B).

When four encoders operate, the transmission bits (4001) are divided infour (referred to as divided bits A, B, C, and D). The first encoderreceives the divided bits A as input, encodes the divided bits A, andoutputs the encoded bits A. The second encoder receives the divided bitsB as input, encodes the divided bits B, and outputs the encoded bits B.The third encoder receives the divided bits C as input, encodes thedivided bits C, and outputs the encoded bits C. The fourth encoderreceives the divided bits D as input, encodes the divided bits D, andoutputs the encoded bits D. The encoded bits A, B, C, and D are dividedinto allocated bits (4003A) and allocated bits (4003B).

The transmission device supports a transmission method such as, forexample, the following Table 1 (Table 1A and Table 1B).

TABLE 1A Number of modulated transmission Pre- signals Error coding(number of Modula- Number correction Trans- matrix transmit tion ofcoding mission hopping antennas) method encoders method informationmethod 1 QPSK 1 A 00000000 — B 00000001 — C 00000010 — 16QAM 1 A00000011 — B 00000100 — C 00000101 — 64QAM 1 A 00000110 — B 00000111 — C00001000 — 256QAM 1 A 00001001 — B 00001010 — C 00001011 — 1024QAM 1 A00001100 — B 00001101 — C 00001110 —

TABLE 1B Number of modulated transmission Error Pre- signals cor- coding(number of Modu- Number rection matrix transmit lation of codingTransmission hopping antennas) method encoders method information method2 #1: QPSK, 1 A 00001111 D #2: QPSK B 00010000 D C 00010001 D 2 A00010010 E B 00010011 E C 00010100 E #1: QPSK, 1 A 00010101 D #2: B00010110 D 16QAM C 00010111 D 2 A 00011000 E B 00011001 E C 00011010 E#1: 1 A 00011011 D 16QAM, B 00011100 D #2: C 00011101 D 16QAM 2 A00011110 E B 00011111 E C 00100000 E #1: 1 A 00100001 D 16QAM, B00100010 D #2: C 00100011 D 64QAM 2 A 00100100 E B 00100101 E C 00100110E #1: 1 A 00100111 F 64QAM, B 00101000 F #2: C 00101001 F 64QAM 2 A00101010 G B 00101011 G C 00101100 G #1: 1 A 00101101 F 64QAM, B00101110 F #2: C 00101111 F 256QAM 2 A 00110000 G B 00110001 G C00110010 G #1: 1 A 00110011 F 256QAM, B 00110100 F #2: C 00110101 F256QAM 2 A 00110110 G B 00110111 G C 00111000 G 4 A 00111001 H B00111010 H C 00111011 H #1: 1 A 00111100 F 256QAM, B 00111101 F #2: C00111110 F 1024QAM 2 A 00111111 G B 01000000 G C 01000001 G 4 A 01000010H B 01000011 H C 01000100 H #1: 1 A 01000101 F 1024QAM, B 01000110 F #2:C 01000111 F 1024QAM 2 A 01001000 G B 01001001 G C 01001010 G 4 A01001011 H B 01001100 H C 01001101 H

As shown in Table 1, transmission of a one-stream signal andtransmission of a two-stream signal are supported as the number oftransmission signals (number of transmit antennas). Furthermore, QPSK,16QAM, 64QAM, 256QAM, and 1024QAM are supported as the modulationmethod. In particular, when the number of transmission signals is two,it is possible to set separate modulation methods for stream #1 andstream #2. For example, “#1: 256QAM, #2: 1024QAM” in Table 1 indicatesthat “the modulation method of stream #1 is 256QAM, and the modulationmethod of stream #2 is 1024QAM” (other entries in the table aresimilarly expressed). Three types of error correction coding methods, A,B, and C, are supported. In this case, A, B, and C may all be differentcoding methods. A, B, and C may also be different coding rates, and A,B, and C may be coding methods with different block sizes.

The pieces of transmission information in Table 1 are allocated to modesthat define a “number of transmission signals”, “modulation method”,“number of encoders”, and “error correction coding method”. Accordingly,in the case of “number of transmission signals: 2”, “modulation method:#1: 1024QAM, #2: 1024QAM”, “number of encoders: 4”, and “errorcorrection coding method: C”, for example, the transmission informationis set to 01001101. In the frame, the transmission device transmits thetransmission information and the transmission data. When transmittingthe transmission data, in particular when the “number of transmissionsignals” is two, a “precoding matrix hopping method” is used inaccordance with Table 1. In Table 1, five types of the “precoding matrixhopping method”, D, E, F, G, and H, are prepared. The precoding matrixhopping method is set to one of these five types in accordance withTable 1. The following, for example, are ways of implementing the fivedifferent types.

Prepare five different precoding matrices.

Use five different types of periods (cycles), for example a four-slotperiod (cycle) for D, an eight-slot period (cycle) for E, . . . .

Use both different precoding matrices and different periods (cycles).

FIG. 41 shows an example of a frame structure of a modulated signaltransmitted by the transmission device in FIG. 40. The transmissiondevice is assumed to support settings for both a mode to transmit twomodulated signals, z1(t) and z2(t), and for a mode to transmit onemodulated signal.

In FIG. 41, the symbol (4100) is a symbol for transmitting the“transmission information” shown in Table 1. The symbols (4101_1) and(4101_2) are reference (pilot) symbols for channel estimation. Thesymbols (4102_1, 4103_1) are data transmission symbols for transmittingthe modulated signal z1(t). The symbols (4102_2, 4103_2) are datatransmission symbols for transmitting the modulated signal z2(t). Thesymbol (4102_1) and the symbol (4102_2) are transmitted at the same timealong the same (shared/common) frequency, and the symbol (4103_1) andthe symbol (4103_2) are transmitted at the same time along the same(shared/common) frequency. The symbols (4102_1, 4103_1) and the symbols(4102_2, 4103_2) are the symbols after precoding matrix calculationusing the method of regularly hopping between precoding matricesdescribed in Embodiments 1-4 and Embodiment 6 (therefore, as describedin Embodiment 1, the structure of the streams s1(t) and s2(t) is as inFIG. 6).

Furthermore, in FIG. 41, the symbol (4104) is a symbol for transmittingthe “transmission information” shown in Table 1. The symbol (4105) is areference (pilot) symbol for channel estimation. The symbols (4106,4107) are data transmission symbols for transmitting the modulatedsignal z1(t). The data transmission symbols for transmitting themodulated signal z1(t) are not precoded, since the number oftransmission signals is one.

Accordingly, the transmission device in FIG. 40 generates and transmitsmodulated signals in accordance with Table 1 and the frame structure inFIG. 41. In FIG. 40, the frame structure signal 313 includes informationregarding the “number of transmission signals”, “modulation method”,“number of encoders”, and “error correction coding method” set based onTable 1. The encoder (4002), the mappers 306A, B, and the weightingunits 308A, B receive the frame structure signal as an input and operatebased on the “number of transmission signals”, “modulation method”,“number of encoders”, and “error correction coding method” that are setbased on Table 1. “Transmission information” corresponding to the set“number of transmission signals”, “modulation method”, “number ofencoders”, and “error correction coding method” is also transmitted tothe reception device.

The structure of the reception device may be represented similarly toFIG. 7 of Embodiment 1. The difference with Embodiment 1 is as follows:since the transmission device and the reception device store theinformation in Table 1 in advance, the transmission device does not needto transmit information for regularly hopping between precodingmatrices, but rather transmits “transmission information” correspondingto the “number of transmission signals”, “modulation method”, “number ofencoders”, and “error correction coding method”, and the receptiondevice obtains information for regularly hopping between precodingmatrices from Table 1 by receiving the “transmission information”.Accordingly, by the control information decoding unit 709 obtaining the“transmission information” transmitted by the transmission device inFIG. 40, the reception device in FIG. 7 obtains, from the informationcorresponding to Table 1, a signal 710 regarding information on thetransmission method, as notified by the transmission device, whichincludes information for regularly hopping between precoding matrices.Therefore, when the number of transmission signals is two, the signalprocessing unit 711 can perform detection based on a precoding matrixhopping pattern to obtain received log-likelihood ratios.

Note that in the above description, “transmission information” is setwith respect to the “number of transmission signals”, “modulationmethod”, “number of encoders”, and “error correction coding method” asin Table 1, and the precoding matrix hopping method is set with respectto the “transmission information”. However, it is not necessary to setthe “transmission information” with respect to the “number oftransmission signals”, “modulation method”, “number of encoders”, and“error correction coding method”. For example, as in Table 2, the“transmission information” may be set with respect to the “number oftransmission signals” and “modulation method”, and the precoding matrixhopping method may be set with respect to the “transmissioninformation”.

TABLE 2 Number of modulated Precoding transmission signals matrix(number of transmit Modulation Transmission hopping antennas) methodinformation method 1 QPSK 00000 — 16QAM 00001 — 64QAM 00010 — 256QAM00011 — 1024QAM 00100 — 2 #1: QPSK, 10000 D #2: QPSK #1: QPSK, 10001 E#2: 16QAM #1: 16QAM, 10010 E #2: 16QAM #1: 16QAM, 10011 E #2: 64QAM #1:64QAM, 10100 F #2: 64QAM #1: 64QAM, 10101 F #2: 256QAM #1: 10110 G256QAM, #2: 256QAM #1: 10111 G 256QAM, #2: 1024QAM #1: 11000 H 1024QAM,#2: 1024QAM

In this context, the “transmission information” and the method ofsetting the precoding matrix hopping method is not limited to Tables 1and 2. As long as a rule is determined in advance for switching theprecoding matrix hopping method based on transmission parameters, suchas the “number of transmission signals”, “modulation method”, “number ofencoders”, “error correction coding method”, or the like (as long as thetransmission device and the reception device share a predetermined rule,or in other words, if the precoding matrix hopping method is switchedbased on any of the transmission parameters (or on any plurality oftransmission parameters)), the transmission device does not need totransmit information regarding the precoding matrix hopping method. Thereception device can identify the precoding matrix hopping method usedby the transmission device by identifying the information on thetransmission parameters and can therefore accurately perform decodingand detection. Note that in Tables 1 and 2, a transmission method thatregularly hops between precoding matrices is used when the number ofmodulated transmission signals is two, but a transmission method thatregularly hops between precoding matrices may be used when the number ofmodulated transmission signals is two or greater.

Accordingly, if the transmission device and reception device share atable regarding transmission patterns that includes information onprecoding hopping methods, the transmission device need not transmitinformation regarding the precoding hopping method, transmitting insteadcontrol information that does not include information regarding theprecoding hopping method, and the reception device can infer theprecoding hopping method by acquiring this control information.

As described above, in the present embodiment, the transmission devicedoes not transmit information directly related to the method ofregularly hopping between precoding matrices. Rather, a method has beendescribed wherein the reception device infers information regardingprecoding for the “method of regularly hopping between precodingmatrices” used by the transmission device. This method yields theadvantageous effect of improved transmission efficiency of data as aresult of the transmission device not transmitting information directlyrelated to the method of regularly hopping between precoding matrices.

Note that the present embodiment has been described as changingprecoding weights in the time domain, but as described in Embodiment 1,the present invention may be similarly embodied when using amulti-carrier transmission method such as OFDM or the like.

In particular, when the precoding hopping method only changes dependingon the number of transmission signals, the reception device can learnthe precoding hopping method by acquiring information, transmitted bythe transmission device, on the number of transmission signals.

In the present description, it is considered that acommunications/broadcasting device such as a broadcast station, a basestation, an access point, a terminal, a mobile phone, or the like isprovided with the transmission device, and that a communications devicesuch as a television, radio, terminal, personal computer, mobile phone,access point, base station, or the like is provided with the receptiondevice. Additionally, it is considered that the transmission device andthe reception device in the present description have a communicationsfunction and are capable of being connected via some sort of interfaceto a device for executing applications for a television, radio, personalcomputer, mobile phone, or the like.

Furthermore, in the present embodiment, symbols other than data symbols,such as pilot symbols (preamble, unique word, postamble, referencesymbol, and the like), symbols for control information, and the like maybe arranged in the frame in any way. While the terms “pilot symbol” and“symbols for control information” have been used here, any term may beused, since the function itself is what is important.

It suffices for a pilot symbol, for example, to be a known symbolmodulated with PSK modulation in the transmission and reception devices(or for the reception device to be able to synchronize in order to knowthe symbol transmitted by the transmission device). The reception deviceuses this symbol for frequency synchronization, time synchronization,channel estimation (estimation of Channel State Information (CSI) foreach modulated signal), detection of signals, and the like.

A symbol for control information is for transmitting information otherthan data (of applications or the like) that needs to be transmitted tothe communication partner for achieving communication (for example, themodulation method, error correction coding method, coding ratio of theerror correction coding method, setting information in the upper layer,and the like).

Note that the present invention is not limited to the above Embodiments1-5 and may be embodied with a variety of modifications. For example,the above embodiments describe communications devices, but the presentinvention is not limited to these devices and may be implemented assoftware for the corresponding communications method.

Furthermore, a precoding hopping method used in a method of transmittingtwo modulated signals from two antennas has been described, but thepresent invention is not limited in this way. The present invention maybe also embodied as a precoding hopping method for similarly changingprecoding weights (matrices) in the context of a method whereby fourmapped signals are precoded to generate four modulated signals that aretransmitted from four antennas, or more generally, whereby N mappedsignals are precoded to generate N modulated signals that aretransmitted from N antennas.

In the description, terms such as “precoding” and “precoding weight” areused, but any other terms may be used. What matters in the presentinvention is the actual signal processing.

Different data may be transmitted in streams s1(t) and s2(t), or thesame data may be transmitted.

Each of the transmit antennas of the transmission device and the receiveantennas of the reception device shown in the figures may be formed by aplurality of antennas.

Programs for executing the above transmission method may, for example,be stored in advance in Read Only Memory (ROM) and be caused to operateby a Central Processing Unit (CPU).

Furthermore, the programs for executing the above transmission methodmay be stored in a computer-readable recording medium, the programsstored in the recording medium may be loaded in the Random Access Memory(RAM) of the computer, and the computer may be caused to operate inaccordance with the programs.

The components in the above embodiments may be typically assembled as aLarge Scale Integration (LSI), a type of integrated circuit. Individualcomponents may respectively be made into discrete chips, or part or allof the components in each embodiment may be made into one chip. While anLSI has been referred to, the terms Integrated Circuit (IC), system LSI,super LSI, or ultra LSI may be used depending on the degree ofintegration. Furthermore, the method for assembling integrated circuitsis not limited to LSI, and a dedicated circuit or a general-purposeprocessor may be used. A Field Programmable Gate Array (FPGA), which isprogrammable after the LSI is manufactured, or a reconfigurableprocessor, which allows reconfiguration of the connections and settingsof circuit cells inside the LSI, may be used.

Furthermore, if technology for forming integrated circuits that replacesLSIs emerges, owing to advances in semiconductor technology or toanother derivative technology, the integration of functional blocks maynaturally be accomplished using such technology. The application ofbiotechnology or the like is possible.

Embodiment 8

The present embodiment describes an application of the method describedin Embodiments 1-4 and Embodiment 6 for regularly hopping betweenprecoding weights.

FIG. 6 relates to the weighting method (precoding method) in the presentembodiment. The weighting unit 600 integrates the weighting units 308Aand 308B in FIG. 3. As shown in FIG. 6, the stream s1(t) and the streams2(t) correspond to the baseband signals 307A and 307B in FIG. 3. Inother words, the streams s1(t) and s2(t) are the baseband signalin-phase components I and quadrature components Q when mapped accordingto a modulation scheme such as QPSK, 16QAM, 64QAM, or the like. Asindicated by the frame structure of FIG. 6, the stream s1(t) isrepresented as s1(u) at symbol number u, as s1(u+1) at symbol numberu+1, and so forth. Similarly, the stream s2(t) is represented as s2(u)at symbol number u, as s2(u+1) at symbol number u+1, and so forth. Theweighting unit 600 receives the baseband signals 307A (s1(t)) and 307B(s2(t)) and the information 315 regarding weighting information in FIG.3 as inputs, performs weighting in accordance with the information 315regarding weighting, and outputs the signals 309A (z1(t)) and 309B(z2(t)) after weighting in FIG. 3.

At this point, when for example a precoding matrix hopping method withan N=8 period (cycle) as in Example #8 in Embodiment 6 is used, z1(t)and z2(t) are represented as follows.

For symbol number 8i (where i is an integer greater than or equal tozero):

$\begin{matrix}{{Equation}\mspace{14mu} 218} & \; \\{\begin{pmatrix}{z\; 1\left( {8i} \right)} \\{z\; 2\left( {8i} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{j\;\pi}{4}}} & {\mathbb{e}}^{j\;{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {8i} \right)} \\{s\; 2\left( {8i} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 228}\end{matrix}$

Here, j is an imaginary unit, and k=0.

For symbol number 8i+1:

$\begin{matrix}{\mspace{76mu}{{Equation}\mspace{14mu} 219}} & \; \\{\begin{pmatrix}{z\; 1\left( {{8i} + 1} \right)} \\{z\; 2\left( {{8i} + 1} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j\;{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 1} \right)} \\{s\; 2\left( {{8i} + 1} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 229}\end{matrix}$

Here, k=1.

For symbol number 8i+2:

$\begin{matrix}{\mspace{76mu}{{Equation}\mspace{14mu} 220}} & \; \\{\begin{pmatrix}{z\; 1\left( {{8i} + 2} \right)} \\{z\; 2\left( {{8i} + 2} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 2} \right)} \\{s\; 2\left( {{8i} + 2} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 230}\end{matrix}$

Here, k=2.

For symbol number 8i+3:

$\begin{matrix}{\mspace{76mu}{{Equation}\mspace{14mu} 221}} & \; \\{\begin{pmatrix}{z\; 1\left( {{8i} + 3} \right)} \\{z\; 2\left( {{8i} + 3} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 3} \right)} \\{s\; 2\left( {{8i} + 3} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 231}\end{matrix}$

Here, k=3.

For symbol number 8i+4:

$\begin{matrix}{\mspace{76mu}{{Equation}\mspace{14mu} 222}} & \; \\{\begin{pmatrix}{z\; 1\left( {{8i} + 4} \right)} \\{z\; 2\left( {{8i} + 4} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 4} \right)} \\{s\; 2\left( {{8i} + 4} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 232}\end{matrix}$

Here, k=4.

For symbol number 8i+5:

$\begin{matrix}{\mspace{76mu}{{Equation}\mspace{14mu} 223}} & \; \\{\begin{pmatrix}{z\; 1\left( {{8i} + 5} \right)} \\{z\; 2\left( {{8i} + 5} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 5} \right)} \\{s\; 2\left( {{8i} + 5} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 233}\end{matrix}$

Here, k=5.

For symbol number 8i+6:

$\begin{matrix}{\mspace{76mu}{{Equation}\mspace{14mu} 224}} & \; \\{\begin{pmatrix}{z\; 1\left( {{8i} + 6} \right)} \\{z\; 2\left( {{8i} + 6} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 6} \right)} \\{s\; 2\left( {{8i} + 6} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 234}\end{matrix}$

Here, k=6.

For symbol number 8i+7:

$\begin{matrix}{\mspace{76mu}{{Equation}\mspace{14mu} 225}} & \; \\{\begin{pmatrix}{z\; 1\left( {{8i} + 7} \right)} \\{z\; 2\left( {{8i} + 7} \right)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j\;\frac{{\mathbb{i}}\;\pi}{4}}} & {\mathbb{e}}^{j{({\frac{k\;\pi}{4} + \frac{7\pi}{8}})}}\end{pmatrix}\begin{pmatrix}{s\; 1\left( {{8i} + 7} \right)} \\{s\; 2\left( {{8i} + 7} \right)}\end{pmatrix}}} & {{Math}\mspace{14mu} 235}\end{matrix}$

Here, k=7.

The symbol numbers shown here can be considered to indicate time. Asdescribed in other embodiments, in Equation 225, for example, z1(8i+7)and z2(8i+7) at time 8i+7 are signals at the same time, and thetransmission device transmits z1(8i+7) and z2(8i+7) over the same(shared/common) frequency. In other words, letting the signals at time Tbe s1(T), s2(T), z1(T), and z2(T), then z1(T) and z2(T) are sought fromsome sort of precoding matrices and from s1(T) and s2(T), and thetransmission device transmits z1(T) and z2(T) over the same(shared/common) frequency (at the same time). Furthermore, in the caseof using a multi-carrier transmission method such as OFDM or the like,and letting signals corresponding to s1, s2, z1, and z2 for (sub)carrierL and time T be s1(T, L), s2(T, L), z1(T, L), and z2(T, L), then z1(T,L) and z2(T, L) are sought from some sort of precoding matrices and froms1(T, L) and s2(T, L), and the transmission device transmits z1(T, L)and z2(T, L) over the same (shared/common) frequency (at the same time).

In this case, the appropriate value of a is given by Equation 198 orEquation 200.

The present embodiment describes a precoding hopping method thatincreases period (cycle) size, based on the above-described precodingmatrices of Equation 190.

Letting the period (cycle) of the precoding hopping method be 8M, 8Mdifferent precoding matrices are represented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 226} & \; \\{{F\left\lbrack {{8 \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \frac{k\;\pi}{4M}})}}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + \frac{k\;\pi}{4M} + \frac{7\;\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 236}\end{matrix}$

In this case, i=0, 1, 2, 3, 4, 5, 6, 7, and k=0, 1, M−2, M−1. Forexample, letting M=2 and α<1, the poor reception points for s1 (∘) andfor s2 (□) at k=0 are represented as in FIG. 42A. Similarly, the poorreception points for s1 (∘) and for s1 (□) at k=1 are represented as inFIG. 42B. In this way, based on the precoding matrices in Equation 190,the poor reception points are as in FIG. 42A, and by using, as theprecoding matrices, the matrices yielded by multiplying each term in thesecond line on the right-hand side of Equation 190 by e^(jX) (seeEquation 225), the poor reception points are rotated with respect toFIG. 42A (see FIG. 42B). (Note that the poor reception points in FIG.42A and FIG. 42B do not overlap. Even when multiplying by e^(jX), thepoor reception points should not overlap, as in this case. Furthermore,the matrices yielded by multiplying each term in the first line on theright-hand side of Equation 189, rather than in the second line on theright-hand side of Equation 190, by e^(jX) may be used as the precodingmatrices.) In this case, the precoding matrices F[0]−F[15] arerepresented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 227} & \; \\{{F\left\lbrack {{8 \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & {\alpha \times {\mathbb{e}}^{j\; 0}} \\{\alpha \times {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + {Xk}})}}} & {\mathbb{e}}^{j{({\frac{{\mathbb{i}}\;\pi}{4} + {Xk} + \frac{7\pi}{8}})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 237}\end{matrix}$

Here, i=0, 1, 2, 3, 4, 5, 6, 7, and k=0, 1.

In this case, when M=2, precoding matrices F[0]−F[15] are generated (theprecoding matrices F[0]−F[15] may be in any order, and the matricesF[0]−F[15] may each be different). Symbol number 16i may be precodedusing F[0], symbol number 16i+1 may be precoded using F[1], . . . , andsymbol number 16i+h may be precoded using F[h], for example (h=0, 1, 2,. . . , 14, 15). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.)

Summarizing the above considerations, with reference to Equations 82-85,N-period (cycle) precoding matrices are represented by the followingequation.

$\begin{matrix}{{Equation}\mspace{14mu} 228} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({\mathbb{i}})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{({\mathbb{i}})}}}} & {{\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \delta})}}\;}\end{pmatrix}}} & {{Math}\mspace{14mu} 238}\end{matrix}$

Here, since the period (cycle) has N slots, i=0, 1, 2, . . . , N−2, N−1.Furthermore, the N×M period (cycle) precoding matrices based on Equation228 are represented by the following equation.

$\begin{matrix}{\mspace{76mu}{{Equation}\mspace{14mu} 229}} & \; \\{{F\left\lbrack {{N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({\mathbb{i}})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + X_{k}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + X_{k} + \lambda + \delta})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 239}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1, and k=0, 1, . . . , M−2, M−1.

Precoding matrices F[0]−F[N×M−1] are thus generated (the precodingmatrices F[0]−F[N×M−1] may be in any order for the N×M slots in theperiod (cycle)). Symbol number N×M×i may be precoded using F[0], symbolnumber N×M×i+1 may be precoded using F[1], . . . , and symbol numberN×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . ,N×M−2, N×M−1). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping method with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality. Note that while the N×M period(cycle) precoding matrices have been set to Equation 229, the N×M period(cycle) precoding matrices may be set to the following equation, asdescribed above.

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 230}} & \; \\{{F\left\lbrack {{N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j(\;{{\theta_{11}{(i)}} + X_{k}})} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + X_{k} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}\;{({\mathbb{i}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \delta})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 240}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1, and k=0, 1, . . . , M−2, M−1.

In Equations 229 and 230, when 0 radians≦δ<2π radians, the matrices area unitary matrix when δ=π radians and are a non-unitary matrix when δ≠πradians. In the present method, use of a non-unitary matrix for π/2radians≦|δ|π radians is one characteristic structure (the conditions forδ being similar to other embodiments), and excellent data receptionquality is obtained. Use of a unitary matrix is another structure, andas described in detail in Embodiment 10 and Embodiment 16, if N is anodd number in Equations 229 and 230, the probability of obtainingexcellent data reception quality increases.

Embodiment 9

The present embodiment describes a method for regularly hopping betweenprecoding matrices using a unitary matrix.

As described in Embodiment 8, in the method of regularly hopping betweenprecoding matrices over a period (cycle) with N slots, the precodingmatrices prepared for the N slots with reference to Equations 82-85 arerepresented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 231} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{(i)}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \delta})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 241}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. (Let α>0.) Since a unitarymatrix is used in the present embodiment, the precoding matrices inEquation 231 may be represented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 232} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({\mathbb{i}})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \pi})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 242}\end{matrix}$

In this case, i=0, 1, 2, . . . , N−2, N−1. (Let α>0.) From Condition #5(Math 106) and Condition #6 (Math 107) in Embodiment 3, the followingcondition is important for achieving excellent data reception quality.Math 243e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #17

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠yMath 244e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #18

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Embodiment 6 describes the distance between poor reception points. Inorder to increase the distance between poor reception points, it isimportant for the number of slots N to be an odd number three orgreater. The following explains this point.

In order to distribute the poor reception points evenly with regards tophase in the complex plane, as described in Embodiment 6, Condition #19and Condition #20 are provided.

$\begin{matrix}{{Condition}\mspace{14mu}{\# 19}} & \; \\{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{(\frac{2\pi}{N})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Math}\mspace{14mu} 245} \\{{Condition}\mspace{14mu}{\# 20}} & \; \\{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\pi}{N}})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Math}\mspace{14mu} 246}\end{matrix}$

In other words, Condition #19 means that the difference in phase is 2π/Nradians. On the other hand, Condition #20 means that the difference inphase is −2π/N radians.

Letting θ₁₁(0)−θ₂₁(0)=0 radians, and letting α<1, the distribution ofpoor reception points for s1 and for s2 in the complex plane for an N=3period (cycle) is shown in FIG. 43A, and the distribution of poorreception points for s1 and for s2 in the complex plane for an N=4period (cycle) is shown in FIG. 43B. Letting θ₁₁−θ₂₁(0)=0 radians, andletting α>1, the distribution of poor reception points for s1 and for s2in the complex plane for an N=3 period (cycle) is shown in FIG. 44A, andthe distribution of poor reception points for s1 and for s2 in thecomplex plane for an N=4 period (cycle) is shown in FIG. 44B.

In this case, when considering the phase between a line segment from theorigin to a poor reception point and a half line along the real axisdefined by real>0 (see FIG. 43A), then for either α>1 or α<1, when N=4,the case always occurs wherein the phase for the poor reception pointsfor s1 and the phase for the poor reception points for s2 are the samevalue. (See 4301, 4302 in FIG. 43B, and 4401, 4402 in FIG. 44B.) In thiscase, in the complex plane, the distance between poor reception pointsbecomes small. On the other hand, when N=3, the phase for the poorreception points for s1 and the phase for the poor reception points fors2 are never the same value.

Based on the above, considering how the case always occurs wherein thephase for the poor reception points for s1 and the phase for the poorreception points for s2 are the same value when the number of slots N inthe period (cycle) is an even number, setting the number of slots N inthe period (cycle) to an odd number increases the probability of agreater distance between poor reception points in the complex plane ascompared to when the number of slots N in the period (cycle) is an evennumber. However, when the number of slots N in the period (cycle) issmall, for example when N≦16, the minimum distance between poorreception points in the complex plane can be guaranteed to be a certainlength, since the number of poor reception points is small. Accordingly,when N≦16, even if N is an even number, cases do exist where datareception quality can be guaranteed.

Therefore, in the method for regularly hopping between precodingmatrices based on Equation 232, when the number of slots N in the period(cycle) is set to an odd number, the probability of improving datareception quality is high. Precoding matrices F[0]−F[N−1] are generatedbased on Equation 232 (the precoding matrices F[0]−F[N−1] may be in anyorder for the N slots in the period (cycle)). Symbol number Ni may beprecoded using F[0], symbol number Ni+1 may be precoded using F[1], . .. , and symbol number N×i+h may be precoded using F[h], for example(h=0, 1, 2, . . . , N−2, N−1). (In this case, as described in previousembodiments, precoding matrices need not be hopped between regularly.)Furthermore, when the modulation method for both s1 and s2 is 16QAM, ifa is set as follows,

$\begin{matrix}{{Equation}\mspace{14mu} 233} & \; \\{\alpha = \frac{\sqrt{2} + 4}{\sqrt{2} + 2}} & {{Math}\mspace{14mu} 247}\end{matrix}$

the advantageous effect of increasing the minimum distance between16×16=256 signal points in the IQ plane for a specific LOS environmentmay be achieved.

In the present embodiment, the method of structuring N differentprecoding matrices for a precoding hopping method with an N-slot timeperiod (cycle) has been described. In this case, as the N differentprecoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] areprepared. In the present embodiment, an example of a single carriertransmission method has been described, and therefore the case ofarranging symbols in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1]in the time domain (or the frequency domain) has been described. Thepresent invention is not, however, limited in this way, and the Ndifferent precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1]generated in the present embodiment may be adapted to a multi-carriertransmission method such as an OFDM transmission method or the like. Asin Embodiment 1, as a method of adaption in this case, precoding weightsmay be changed by arranging symbols in the frequency domain and in thefrequency-time domain. Note that a precoding hopping method with anN-slot time period (cycle) has been described, but the same advantageouseffects may be obtained by randomly using N different precodingmatrices. In other words, the N different precoding matrices do notnecessarily need to be used in a regular period (cycle).

Furthermore, in the precoding matrix hopping method over an H-slotperiod (cycle) (H being a natural number larger than the number of slotsN in the period (cycle) of the above method of regularly hopping betweenprecoding matrices), when the N different precoding matrices of thepresent embodiment are included, the probability of excellent receptionquality increases. In this case, Condition #17 and Condition #18 can bereplaced by the following conditions. (The number of slots in the period(cycle) is considered to be N.)Math 248e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∃x,∃y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #17′

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 249e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∃x,∃y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #18′

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Embodiment 10

The present embodiment describes a method for regularly hopping betweenprecoding matrices using a unitary matrix that differs from the examplein Embodiment 9.

In the method of regularly hopping between precoding matrices over aperiod (cycle) with 2N slots, the precoding matrices prepared for the 2Nslots are represented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 234} & \; \\{{{{{for}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({\mathbb{i}})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \pi})}}\end{pmatrix}}}} & {{Math}\mspace{14mu} 250}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0.

$\begin{matrix}{{Equation}\mspace{14mu} 235} & \; \\{{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;{\theta_{11}{({\mathbb{i}})}}}} & {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({\mathbb{i}})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \pi})}}}\end{pmatrix}}}} & {{Math}\mspace{14mu} 251}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. (Let the α inEquation 234 and the α in Equation 235 be the same value.)

From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment3, the following conditions are important in Equation 234 for achievingexcellent data reception quality.Math 252e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #21

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 253e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #22

(x is 0, 1, 2, . . . , N−2, N−1; y is

Addition of the following condition is considered.Math 254θ₁₁(x)=θ₁₁(x+N) for ∀x(x=0,1,2, . . . ,N−2,N−1)andθ₂₁(y)=θ₂₁(y+N) for ∀y(y=0,1,2, . . . ,N−2,N−1)  Condition #23

Next, in order to distribute the poor reception points evenly withregards to phase in the complex plane, as described in Embodiment 6,Condition #24 and Condition #25 are provided.

$\begin{matrix}{{Condition}\mspace{14mu}{\# 24}} & \; \\{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{(\frac{2\pi}{N})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Math}\mspace{14mu} 255} \\{{Condition}\mspace{14mu}{\# 25}} & \; \\{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\pi}{N\;}})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Math}\mspace{14mu} 256}\end{matrix}$

In other words, Condition #24 means that the difference in phase is 2π/Nradians. On the other hand, Condition #25 means that the difference inphase is −2π/N radians.

Letting θ₁₁(0)−θ₂₁(0)=0 radians, and letting α>1, the distribution ofpoor reception points for s1 and for s2 in the complex plane when N=4 isshown in FIGS. 45A and 45B. As is clear from FIGS. 45A and 45B, in thecomplex plane, the minimum distance between poor reception points for s1is kept large, and similarly, the minimum distance between poorreception points for s2 is also kept large.

Similar conditions are created when α<1. Furthermore, making the sameconsiderations as in Embodiment 9, the probability of a greater distancebetween poor reception points in the complex plane increases when N isan odd number as compared to when N is an even number. However, when Nis small, for example when N≦16, the minimum distance between poorreception points in the complex plane can be guaranteed to be a certainlength, since the number of poor reception points is small. Accordingly,when N≦16, even if N is an even number, cases do exist where datareception quality can be guaranteed.

Therefore, in the method for regularly hopping between precodingmatrices based on Equations 234 and 235, when N is set to an odd number,the probability of improving data reception quality is high. Precodingmatrices F[0]−F[2N−1] are generated based on Equations 234 and 235 (theprecoding matrices F[0]−F[2N−1] may be arranged in any order for the 2Nslots in the period (cycle)). Symbol number 2Ni may be precoded usingF[0], symbol number 2Ni+1 may be precoded using F[1], . . . , and symbolnumber 2N×i+h may be precoded using F[h], for example (h=0, 1, 2, . . ., 2N−2, 2N−1). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.) Furthermore,when the modulation method for both s1 and s2 is 16QAM, if a is set asin Equation 233, the advantageous effect of increasing the minimumdistance between 16×16=256 signal points in the IQ plane for a specificLOS environment may be achieved.

The following conditions are possible as conditions differing fromCondition #23:Math 257e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)  Condition #26

(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . ,2N−2, 2N−1; and x≠y.)Math 258e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)  Condition #27

(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . ,2N−2, 2N−1; and x # y.)

In this case, by satisfying Condition #21, Condition #22, Condition #26,and Condition #27, the distance in the complex plane between poorreception points for s1 is increased, as is the distance between poorreception points for s2, thereby achieving excellent data receptionquality.

In the present embodiment, the method of structuring 2N differentprecoding matrices for a precoding hopping method with a 2N-slot timeperiod (cycle) has been described. In this case, as the 2N differentprecoding matrices, F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] areprepared. In the present embodiment, an example of a single carriertransmission method has been described, and therefore the case ofarranging symbols in the order F[0], F[1], F[2], . . . , F[2N−2],F[2N−1] in the time domain (or the frequency domain) has been described.The present invention is not, however, limited in this way, and the 2Ndifferent precoding matrices F[0], F[1], F[2], . . . , F[2N−2], F[2N−1]generated in the present embodiment may be adapted to a multi-carriertransmission method such as an OFDM transmission method or the like. Asin Embodiment 1, as a method of adaption in this case, precoding weightsmay be changed by arranging symbols in the frequency domain and in thefrequency-time domain. Note that a precoding hopping method with a2N-slot time period (cycle) has been described, but the sameadvantageous effects may be obtained by randomly using 2N differentprecoding matrices. In other words, the 2N different precoding matricesdo not necessarily need to be used in a regular period (cycle).

Furthermore, in the precoding matrix hopping method over an H-slotperiod (cycle) (H being a natural number larger than the number of slots2N in the period (cycle) of the above method of regularly hoppingbetween precoding matrices), when the 2N different precoding matrices ofthe present embodiment are included, the probability of excellentreception quality increases.

Embodiment 11

The present embodiment describes a method for regularly hopping betweenprecoding matrices using a non-unitary matrix.

In the method of regularly hopping between precoding matrices over aperiod (cycle) with 2N slots, the precoding matrices prepared for the 2Nslots are represented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 236} & \; \\{{{{{for}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({\mathbb{i}})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \delta})}}\end{pmatrix}}}} & {{Math}\mspace{14mu} 259}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. Furthermore, letδ≠π radians.

$\begin{matrix}{{Equation}\mspace{14mu} 237} & \; \\{{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}\;}} & {\mathbb{e}}^{{j\theta}_{11}{({\mathbb{i}})}} \\{\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \delta})}} & {\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}}}\end{pmatrix}}}} & {{Math}\mspace{14mu} 260}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. (Let the α inEquation 236 and the α in Equation 237 be the same value.)

From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment3, the following conditions are important in Equation 236 for achievingexcellent data reception quality.Math 261e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #28

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 262e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−δ)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−δ)) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #29

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Addition of the following condition is considered.Math 263θ₁₁(x)=θ₁₁(x+N) for ∀x(x=0,1,2, . . . ,N−2,N−1)andθ₂₁(y)=θ₂₁(y+N) for ∀y(y=0,1,2, . . . ,N−2,N−1)  Condition #30

Note that instead of Equation 237, the precoding matrices in thefollowing Equation may be provided.

$\begin{matrix}{{Equation}\mspace{14mu} 238} & \; \\{{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}\;}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j\;{\theta_{11}{({\mathbb{i}})}}}} & {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({\mathbb{i}})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda - \delta})}}}\end{pmatrix}}}} & {{Math}\mspace{14mu} 264}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. (Let the α inEquation 236 and the α in Equation 238 be the same value.) As anexample, in order to distribute the poor reception points evenly withregards to phase in the complex plane, as described in Embodiment 6,Condition #31 and Condition #32 are provided.

$\begin{matrix}{{Condition}\mspace{14mu}{\# 31}} & \; \\{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{(\frac{2\pi}{N})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Math}\mspace{14mu} 265} \\{{Condition}\mspace{14mu}{\# 32}} & \; \\{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\pi}{N}})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Math}\mspace{14mu} 266}\end{matrix}$

In other words, Condition #31 means that the difference in phase is 2π/Nradians. On the other hand, Condition #32 means that the difference inphase is −2π/N radians.

Letting θ₁₁(0)−θ₂₁(0)=0 radians, letting α>1, and letting 6=(3π)/4radians, the distribution of poor reception points for s1 and for s2 inthe complex plane when N=4 is shown in FIGS. 46A and 46B. With thesesettings, the period (cycle) for hopping between precoding matrices isincreased, and the minimum distance between poor reception points fors1, as well as the minimum distance between poor reception points fors2, in the complex plane is kept large, thereby achieving excellentreception quality. An example in which α>1, δ=(3π)/4 radians, and N=4has been described, but the present invention is not limited in thisway. Similar advantageous effects may be obtained for π/2 radians≦|δ|πradians, α>0, and α≠1.

The following conditions are possible as conditions differing fromCondition #30:Math 267e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)  Condition #33(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . ,2N−2, 2N−1; and x≠y.)Math 268e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)  Condition #34

(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . ,2N−2, 2N−1; and x≠y.)

In this case, by satisfying Condition #28, Condition #29, Condition #33,and Condition #34, the distance in the complex plane between poorreception points for s1 is increased, as is the distance between poorreception points for s2, thereby achieving excellent data receptionquality.

In the present embodiment, the method of structuring 2N differentprecoding matrices for a precoding hopping method with a 2N-slot timeperiod (cycle) has been described. In this case, as the 2N differentprecoding matrices, F[0], F[1], F[2], F[2N−2], F[2N−1] are prepared. Inthe present embodiment, an example of a single carrier transmissionmethod has been described, and therefore the case of arranging symbolsin the order F[0], F[1], F[2], F[2N−2], F[2N−1] in the time domain (orthe frequency domain) has been described. The present invention is not,however, limited in this way, and the 2N different precoding matricesF[0], F[1], F[2], F[2N−2], F[2N−1] generated in the present embodimentmay be adapted to a multi-carrier transmission method such as an OFDMtransmission method or the like. As in Embodiment 1, as a method ofadaption in this case, precoding weights may be changed by arrangingsymbols in the frequency domain and in the frequency-time domain. Notethat a precoding hopping method with a 2N-slot time period (cycle) hasbeen described, but the same advantageous effects may be obtained byrandomly using 2N different precoding matrices. In other words, the 2Ndifferent precoding matrices do not necessarily need to be used in aregular period (cycle).

Furthermore, in the precoding matrix hopping method over an H-slotperiod (cycle) (H being a natural number larger than the number of slots2N in the period (cycle) of the above method of regularly hoppingbetween precoding matrices), when the 2N different precoding matrices ofthe present embodiment are included, the probability of excellentreception quality increases.

Embodiment 12

The present embodiment describes a method for regularly hopping betweenprecoding matrices using a non-unitary matrix.

In the method of regularly hopping between precoding matrices over aperiod (cycle) with N slots, the precoding matrices prepared for the Nslots are represented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 239} & \; \\{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({\mathbb{i}})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{({\mathbb{i}})}}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \delta})}}\end{pmatrix}}} & {{Math}\mspace{14mu} 269}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. Furthermore, letδ≠π radians (a fixed value not depending on i), and i=0, 1, 2, . . . ,N−2, N−1.

From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment3, the following conditions are important in Equation 239 for achievingexcellent data reception quality.Math 270e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #35(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 271e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−δ)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−δ)) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #36(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

As an example, in order to distribute the poor reception points evenlywith regards to phase in the complex plane, as described in Embodiment6, Condition #37 and Condition #38 are provided.

$\begin{matrix}{{Condition}\mspace{14mu}{\# 37}} & \; \\{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{(\frac{2\pi}{N})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Math}\mspace{14mu} 272} \\{{Condition}\mspace{14mu}{\# 38}} & \; \\{{\frac{{\mathbb{e}}^{{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}\;}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\pi}{N}})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Math}\mspace{14mu} 273}\end{matrix}$

In other words, Condition #37 means that the difference in phase is 2π/Nradians. On the other hand, Condition #38 means that the difference inphase is −2π/N radians.

In this case, if π/2 radians≦|δ|<π radians, α>0, and α≠1, the distancein the complex plane between poor reception points for s1 is increased,as is the distance between poor reception points for s2, therebyachieving excellent data reception quality. Note that Condition #37 andCondition #38 are not always necessary.

In the present embodiment, the method of structuring N differentprecoding matrices for a precoding hopping method with an N-slot timeperiod (cycle) has been described. In this case, as the N differentprecoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] areprepared. In the present embodiment, an example of a single carriertransmission method has been described, and therefore the case ofarranging symbols in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1]in the time domain (or the frequency domain) has been described. Thepresent invention is not, however, limited in this way, and the Ndifferent precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1]generated in the present embodiment may be adapted to a multi-carriertransmission method such as an OFDM transmission method or the like. Asin Embodiment 1, as a method of adaption in this case, precoding weightsmay be changed by arranging symbols in the frequency domain and in thefrequency-time domain. Note that a precoding hopping method with anN-slot time period (cycle) has been described, but the same advantageouseffects may be obtained by randomly using N different precodingmatrices. In other words, the N different precoding matrices do notnecessarily need to be used in a regular period (cycle).

Furthermore, in the precoding matrix hopping method over an H-slotperiod (cycle) (H being a natural number larger than the number of slotsN in the period (cycle) of the above method of regularly hopping betweenprecoding matrices), when the N different precoding matrices of thepresent embodiment are included, the probability of excellent receptionquality increases. In this case, Condition #35 and Condition #36 can bereplaced by the following conditions. (The number of slots in the period(cycle) is considered to be N.)Math 274e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∃x,∃y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #35′

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠yMath 275e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−δ)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−δ)) for∃x,∃y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #36′

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Embodiment 13

The present embodiment describes a different example than Embodiment 8.

In the method of regularly hopping between precoding matrices over aperiod (cycle) with 2N slots, the precoding matrices prepared for the 2Nslots are represented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 240} & \; \\{{{{{for}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({\mathbb{i}})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j\;{\theta_{21}{({\mathbb{i}})}}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \delta})}}\end{pmatrix}}}} & {{Math}\mspace{14mu} 276}\end{matrix}$Let α be a fixed value (not depending on i), where α>0. Furthermore, letδ≠π radians.

$\begin{matrix}{{Equation}\mspace{14mu} 241} & \; \\{{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} & {\mathbb{e}}^{{j\theta}_{11}{({\mathbb{i}})}} \\{\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \delta})}} & {\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}}}\end{pmatrix}}}} & {{Math}\mspace{14mu} 277}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. (Let the α inEquation 240 and the α in Equation 241 be the same value.)

Furthermore, the 2×N×M period (cycle) precoding matrices based onEquations 240 and 241 are represented by the following equations.

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 242}} & \; \\{\mspace{79mu}{{{{{for}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{11}{({\mathbb{i}})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + X_{k}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + X_{k} + \lambda + \delta})}}\end{pmatrix}}}}} & {{Math}\mspace{14mu} 278}\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 243}} & \; \\{\mspace{79mu}{{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} & {\mathbb{e}}^{{j\theta}_{11}{({\mathbb{i}})}} \\{\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \delta + Y_{k}})}} & {\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({{\mathbb{i}} + Y_{k}})}}}\end{pmatrix}}}}} & {{Math}\mspace{14mu} 279}\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1. Furthermore, Xk=Yk may be true,or Xk≠Yk may be true.

Precoding matrices F[0]−F[2×N×M−1] are thus generated (the precodingmatrices F[0]−F[2×N×M−1] may be in any order for the 2×N×M slots in theperiod (cycle)). Symbol number 2×N×M×i may be precoded using F[0],symbol number 2×N×M×i+1 may be precoded using F[1], . . . , and symbolnumber 2×N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . .. , 2×N×M−2, 2×N×M−1). (In this case, as described in previousembodiments, precoding matrices need not be hopped between regularly.)

Generating the precoding matrices in this way achieves a precodingmatrix hopping method with a large period (cycle), allowing for theposition of poor reception points to be easily changed, which may leadto improved data reception quality.

The 2×N×M period (cycle) precoding matrices in Equation 242 may bechanged to the following equation.

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 244}} & \; \\{\mspace{79mu}{{{{{for}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + X_{k}})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + X_{k} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \delta})}}\end{pmatrix}}}}} & {{Math}\mspace{14mu} 280}\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

The 2×N×M period (cycle) precoding matrices in Equation 243 may also bechanged to any of Equations 245-247.

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 245}} & \; \\{\mspace{79mu}{{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda + Y_{k}})}}} & {\mathbb{e}}^{j\;{\theta_{11}{({{\mathbb{i}} + Y_{k}})}}} \\{\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \delta})}} & {\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}}}\end{pmatrix}}}}} & {{Math}\mspace{14mu} 281}\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 246}} & \; \\{\mspace{79mu}{{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{{j\theta}_{11}{({\mathbb{i}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}({{\mathbb{i}} + Y_{k}}\;)} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda - \delta + Y_{k}})}}}\end{pmatrix}}}}} & {{Math}\mspace{14mu} 282}\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 247}} & \; \\{\mspace{79mu}{{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\left\lbrack {{2 \times N \times k} + i} \right\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{{j\theta}_{11}{({{\mathbb{i}} + Y_{k}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda + Y_{k}})}} \\{\mathbb{e}}^{j\;{\theta_{21}{({\mathbb{i}})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda - \delta})}}}\end{pmatrix}}}}} & {{Math}\mspace{14mu} 283}\end{matrix}$

In this case, k=0, 1, . . . , M−2, M−1.

Focusing on poor reception points, if Equations 242 through 247 satisfythe following conditions,Math 284e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #39

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 285e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−δ)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−δ)) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #40

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 286θ₁₁(x)=θ₁₁(x+N) for ∀x(x=0,1,2, . . . ,N−2,N−1)andθ₂₁(y)=θ₂₁(y+N) for ∀y(y=0,1,2, . . . ,N−2,N−1)  Condition #41

then excellent data reception quality is achieved. Note that inEmbodiment 8, Condition #39 and Condition #40 should be satisfied.

Focusing on Xk and Yk, if Equations 242 through 247 satisfy thefollowing conditions,Math 287X _(a) ≠X _(b)+2×s×π for ∀a,∀b(a≠b;a,b=0,1,2, . . . ,M−2,M−1  Condition#42

(a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1; anda≠b.)

(Here, s is an integer.)Math 288Y _(a) ≠Y _(b)+2×u×π for ∀a,∀b(a≠b;a,b=0,1,2, . . . ,M−2,M−1  Condition#43

(a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1; anda≠b.)

(Here, u is an integer.)

then excellent data reception quality is achieved. Note that inEmbodiment 8, Condition #42 should be satisfied.

In Equations 242 and 247, when 0 radians≦δ<2π radians, the matrices area unitary matrix when δ=π radians and are a non-unitary matrix when δ≠πradians. In the present method, use of a non-unitary matrix for π/2radians≦|δ|π radians is one characteristic structure, and excellent datareception quality is obtained. Use of a unitary matrix is anotherstructure, and as described in detail in Embodiment 10 and Embodiment16, if N is an odd number in Equations 242 through 247, the probabilityof obtaining excellent data reception quality increases.

Embodiment 14

The present embodiment describes an example of differentiating betweenusage of a unitary matrix and a non-unitary matrix as the precodingmatrix in the method for regularly hopping between precoding matrices.

The following describes an example that uses a two-by-two precodingmatrix (letting each element be a complex number), i.e. the case whentwo modulated signals (s1(t) and s2(t)) that are based on a modulationmethod are precoded, and the two precoded signals are transmitted by twoantennas.

When transmitting data using a method of regularly hopping betweenprecoding matrices, the mappers 306A and 306B in the transmission devicein FIG. 3 and FIG. 13 switch the modulation method in accordance withthe frame structure signal 313. The relationship between the modulationlevel (the number of signal points for the modulation method in the IQplane) of the modulation method and the precoding matrices is described.

The advantage of the method of regularly hopping between precodingmatrices is that, as described in Embodiment 6, excellent data receptionquality is achieved in an LOS environment. In particular, when thereception device performs ML calculation or applies APP (or Max-log APP)based on ML calculation, the advantageous effect is considerable.Incidentally, ML calculation greatly impacts circuit scale (calculationscale) in accordance with the modulation level of the modulation method.For example, when two precoded signals are transmitted from twoantennas, and the same modulation method is used for two modulatedsignals (signals based on the modulation method before precoding), thenumber of candidate signal points in the IQ plane (received signalpoints 1101 in FIG. 11) is 4×4=16 when the modulation method is QPSK,16×16=256 when the modulation method is 16QAM, 64×64=4096 when themodulation method is 64QAM, 256×256=65,536 when the modulation method is256QAM, and 1024×1024=1,048,576 when the modulation method is 256QAM. Inorder to keep the calculation scale of the reception device down to acertain circuit size, when the modulation method is QPSK, 16QAM, or64QAM, ML calculation ((Max-log) APP based on ML calculation) is used,and when the modulation method is 256QAM or 1024QAM, linear operationsuch as MMSE or ZF is used in the reception device. (In some cases, MLcalculation may be used for 256QAM.)

When such a reception device is assumed, consideration of theSignal-to-Noise power Ratio (SNR) after separation of multiple signalsindicates that a unitary matrix is appropriate as the precoding matrixwhen the reception device performs linear operation such as MMSE or ZF,whereas either a unitary matrix or a non-unitary matrix may be used whenthe reception device performs ML calculation. Taking any of the aboveembodiments into consideration, when two precoded signals aretransmitted from two antennas, the same modulation method is used fortwo modulated signals (signals based on the modulation method beforeprecoding), a non-unitary matrix is used as the precoding matrix in themethod for regularly hopping between precoding matrices, the modulationlevel of the modulation method is equal to or less than 64 (or equal toor less than 256), and a unitary matrix is used when the modulationlevel is greater than 64 (or greater than 256), then for all of themodulation methods supported by the transmission system, there is anincreased probability of achieving the advantageous effect wherebyexcellent data reception quality is achieved for any of the modulationmethods while reducing the circuit scale of the reception device.

When the modulation level of the modulation method is equal to or lessthan 64 (or equal to or less than 256) as well, in some cases use of aunitary matrix may be preferable. Based on this consideration, when aplurality of modulation methods are supported in which the modulationlevel is equal to or less than 64 (or equal to or less than 256), it isimportant that in some cases, in some of the plurality of supportedmodulation methods where the modulation level is equal to or less than64, a non-unitary matrix is used as the precoding matrix in the methodfor regularly hopping between precoding matrices.

The case of transmitting two precoded signals from two antennas has beendescribed above as an example, but the present invention is not limitedin this way. In the case when N precoded signals are transmitted from Nantennas, and the same modulation method is used for N modulated signals(signals based on the modulation method before precoding), a thresholdβ_(N) may be established for the modulation level of the modulationmethod. When a plurality of modulation methods for which the modulationlevel is equal to or less than β_(N) are supported, in some of theplurality of supported modulation methods where the modulation level isequal to or less than β_(N), a non-unitary matrix is used as theprecoding matrices in the method for regularly hopping between precodingmatrices, whereas for modulation methods for which the modulation levelis greater than β_(N), a unitary matrix is used. In this way, for all ofthe modulation methods supported by the transmission system, there is anincreased probability of achieving the advantageous effect wherebyexcellent data reception quality is achieved for any of the modulationmethods while reducing the circuit scale of the reception device. (Whenthe modulation level of the modulation method is equal to or less thanβ_(N), a non-unitary matrix may always be used as the precoding matrixin the method for regularly hopping between precoding matrices.)

In the above description, the same modulation method has been describedas being used in the modulation method for simultaneously transmitting Nmodulated signals. The following, however, describes the case in whichtwo or more modulation methods are used for simultaneously transmittingN modulated signals.

As an example, the case in which two precoded signals are transmitted bytwo antennas is described. The two modulated signals (signals based onthe modulation method before precoding) are either modulated with thesame modulation method, or when modulated with different modulationmethods, are modulated with a modulation method having a modulationlevel of 2^(a1) or a modulation level of 2^(a2). In this case, when thereception device uses ML calculation ((Max-log) APP based on MLcalculation), the number of candidate signal points in the IQ plane(received signal points 1101 in FIG. 11) is 2^(a1)×2^(a2)=2^(a1+a2). Asdescribed above, in order to achieve excellent data reception qualitywhile reducing the circuit scale of the reception device, a threshold2^(β) may be provided for 2^(a1+a2), and when 2^(a1+a2)≦2^(β), anon-unitary matrix may be used as the precoding matrix in the method forregularly hopping between precoding matrices, whereas a unitary matrixmay be used when 2^(a1+a2)>2^(β).

Furthermore, when 2^(a1+a2)≦2^(β), in some cases use of a unitary matrixmay be preferable. Based on this consideration, when a plurality ofcombinations of modulation methods are supported for which2^(a1+a2)≦2^(β), it is important that in some of the supportedcombinations of modulation methods for which 2^(a1+a2)≦2^(β), anon-unitary matrix is used as the precoding matrix in the method forregularly hopping between precoding matrices.

As an example, the case in which two precoded signals are transmitted bytwo antennas has been described, but the present invention is notlimited in this way. For example, N modulated signals (signals based onthe modulation method before precoding) may be either modulated with thesame modulation method or, when modulated with different modulationmethods, the modulation level of the modulation method for the i^(th)modulated signal may be 2^(ai) (where i=1, 2, . . . , N−1, N).

In this case, when the reception device uses ML calculation ((Max-log)APP based on ML calculation), the number of candidate signal points inthe IQ plane (received signal points 1101 in FIG. 11) is 2^(a1)×2^(a2)×. . . ×2^(a1)× . . . ×2^(aN)=2^(a1+a2+ . . . +ai+ . . . +aN). Asdescribed above, in order to achieve excellent data reception qualitywhile reducing the circuit scale of the reception device, a threshold2^(β) may be provided for 2^(a1+a2+ . . . +ai+ . . . +aN).

$\begin{matrix}{{Condition}\mspace{14mu}{\# 44}} & \; \\{{2^{{a\; 1} + {a\; 2} + \ldots + {ai} + \ldots + {aN}} = {2^{Y} \leq 2^{\beta}}}{where}{Y = {\sum\limits_{i = 1}^{N}a_{i}}}} & {{Math}\mspace{14mu} 289}\end{matrix}$

When a plurality of combinations of a modulation methods satisfyingCondition #44 are supported, in some of the supported combinations ofmodulation methods satisfying Condition #44, a non-unitary matrix areused as the precoding matrix in the method for regularly hopping betweenprecoding matrices.

$\begin{matrix}{{Condition}\mspace{14mu}{\# 45}} & \; \\{{2^{{a\; 1} + {a\; 2} + \ldots + {ai} + \ldots + {aN}} = {2^{Y} > 2^{\beta}}}{where}{Y = {\sum\limits_{i = 1}^{N}a_{i}}}} & {{Math}\mspace{14mu} 290}\end{matrix}$

By using a unitary matrix in all of the combinations of modulationmethods satisfying Condition #45, then for all of the modulation methodssupported by the transmission system, there is an increased probabilityof achieving the advantageous effect whereby excellent data receptionquality is achieved while reducing the circuit scale of the receptiondevice for any of the combinations of modulation methods. (A non-unitarymatrix may be used as the precoding matrix in the method for regularlyhopping between precoding matrices in all of the supported combinationsof modulation methods satisfying Condition #44.)

Embodiment 15

The present embodiment describes an example of a system that adopts amethod for regularly hopping between precoding matrices using amulti-carrier transmission method such as OFDM.

FIGS. 47A and 47B show an example according to the present embodiment offrame structure in the time and frequency domains for a signaltransmitted by a broadcast station (base station) in a system thatadopts a method for regularly hopping between precoding matrices using amulti-carrier transmission method such as OFDM. (The frame structure isset to extend from time $1 to time $T.) FIG. 47A shows the framestructure in the time and frequency domains for the stream s1 describedin Embodiment 1, and FIG. 47B shows the frame structure in the time andfrequency domains for the stream s2 described in Embodiment 1. Symbolsat the same time and the same (sub)carrier in stream s1 and stream s2are transmitted by a plurality of antennas at the same time and the samefrequency.

In FIGS. 47A and 47B, the (sub)carriers used when using OFDM are dividedas follows: a carrier group #A composed of (sub)carrier a−(sub)carriera+Na, a carrier group #B composed of (sub)carrier b−(sub)carrier b+Nb, acarrier group #C composed of (sub)carrier c−(sub)carrier c+Nc, a carriergroup #D composed of (sub)carrier d−(sub)carrier d+Nd, . . . . In eachsubcarrier group, a plurality of transmission methods are assumed to besupported. By supporting a plurality of transmission methods, it ispossible to effectively capitalize on the advantages of the transmissionmethods. For example, in FIGS. 47A and 47B, a spatial multiplexing MIMOsystem, or a MIMO system with a fixed precoding matrix is used forcarrier group #A, a MIMO system that regularly hops between precodingmatrices is used for carrier group #B, only stream s1 is transmitted incarrier group #C, and space-time block coding is used to transmitcarrier group #D.

FIGS. 48A and 48B show an example according to the present embodiment offrame structure in the time and frequency domains for a signaltransmitted by a broadcast station (base station) in a system thatadopts a method for regularly hopping between precoding matrices using amulti-carrier transmission method such as OFDM. FIGS. 48A and 48B show aframe structure at a different time than FIGS. 47A and 47B, from time $Xto time $X+T′. In FIGS. 48A and 48B, as in FIGS. 47A and 47B, the(sub)carriers used when using OFDM are divided as follows: a carriergroup #A composed of (sub)carrier a−(sub)carrier a+Na, a carrier group#B composed of (sub)carrier b−(sub)carrier b+Nb, a carrier group #Ccomposed of (sub)carrier c−(sub)carrier c+Nc, a carrier group #Dcomposed of (sub)carrier d−(sub)carrier d+Nd, . . . . The differencebetween FIGS. 47A and 47B and FIGS. 48A and 48B is that in some carriergroups, the transmission method used in FIGS. 47A and 47B differs fromthe transmission method used in FIGS. 48A and 48B. In FIGS. 48A and 48B,space-time block coding is used to transmit carrier group #A, a MIMOsystem that regularly hops between precoding matrices is used forcarrier group #B, a MIMO system that regularly hops between precodingmatrices is used for carrier group #C, and only stream s1 is transmittedin carrier group #D.

Next, the supported transmission methods are described.

FIG. 49 shows a signal processing method when using a spatialmultiplexing MIMO system or a MIMO system with a fixed precoding matrix.FIG. 49 bears the same numbers as in FIG. 6.

A weighting unit 600, which is a baseband signal in accordance with acertain modulation method, receives as inputs a stream s1(t) (307A), astream s2(t) (307B), and information 315 regarding the weighting method,and outputs a modulated signal z1(t) (309A) after weighting and amodulated signal z2(t) (309B) after weighting. Here, when theinformation 315 regarding the weighting method indicates a spatialmultiplexing MIMO system, the signal processing in method #1 of FIG. 49is performed. Specifically, the following processing is performed.

$\begin{matrix}{{Equation}\mspace{14mu} 250} & \; \\\begin{matrix}{\begin{pmatrix}{z\; 1(t)} \\{z\; 2(t)}\end{pmatrix} = {\begin{pmatrix}{\mathbb{e}}^{j\; 0} & 0 \\0 & {\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{s\; 1(t)} \\{s\; 2(t)}\end{pmatrix}}} \\{= {{\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}\begin{pmatrix}{s\; 1(t)} \\{s\; 2(t)}\end{pmatrix}} = \begin{pmatrix}{s\; 1(t)} \\{s\; 2(t)}\end{pmatrix}}}\end{matrix} & {{Math}\mspace{14mu} 291}\end{matrix}$

When a method for transmitting one modulated signal is supported, fromthe standpoint of transmission power, Equation 250 may be represented asEquation 251.

$\begin{matrix}{{Equation}\mspace{14mu} 251} & \; \\\begin{matrix}{\begin{pmatrix}{z\; 1(t)} \\{z\; 2(t)}\end{pmatrix} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; 0} & 0 \\0 & {\mathbb{e}}^{j\; 0}\end{pmatrix}\begin{pmatrix}{s\; 1(t)} \\{s\; 2(t)}\end{pmatrix}}} \\{= {{\frac{1}{\sqrt{2}}\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}\begin{pmatrix}{s\; 1(t)} \\{s\; 2(t)}\end{pmatrix}} = \begin{pmatrix}{\frac{1}{\sqrt{2}}s\; 1(t)} \\{\frac{1}{\sqrt{2}\;}s\; 2(t)}\end{pmatrix}}}\end{matrix} & {{Math}\mspace{14mu} 292}\end{matrix}$

When the information 315 regarding the weighting method indicates a MIMOsystem in which precoding matrices are regularly hopped between, signalprocessing in method #2, for example, of FIG. 49 is performed.Specifically, the following processing is performed.

$\begin{matrix}{{Equation}\mspace{14mu} 252} & \; \\{\begin{pmatrix}{z\; 1(t)} \\{z\; 2(t)}\end{pmatrix} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;\theta_{11}} & {\alpha \times {\mathbb{e}}^{j{({\theta_{11} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}}} & {\mathbb{e}}^{j{({\theta_{21} + \lambda + \delta})}}\end{pmatrix}\begin{pmatrix}{s\; 1(t)} \\{s\; 2(t)}\end{pmatrix}}} & {{Math}\mspace{14mu} 293}\end{matrix}$

Here, θ₁₁, θ₁₂, λ, and δ are fixed values.

FIG. 50 shows the structure of modulated signals when using space-timeblock coding. A space-time block coding unit (5002) in FIG. 50 receives,as input, a baseband signal based on a certain modulation signal. Forexample, the space-time block coding unit (5002) receives symbol s1,symbol s2, . . . as inputs. As shown in FIG. 50, space-time block codingis performed, z1(5003A) becomes “s1 as symbol #0”, “−s2* as symbol #0”,“s3 as symbol #2”, “−s4* as symbol #3” . . . , and z2(5003B) becomes “s2as symbol #0”, “s1* as symbol #1”, “s4 as symbol #2”, “s3* as symbol #3”. . . . In this case, symbol #X in z1 and symbol #X in z2 aretransmitted from the antennas at the same time, over the same frequency.

In FIGS. 47A, 47B, 48A, and 48B, only symbols transmitting data areshown. In practice, however, it is necessary to transmit informationsuch as the transmission method, modulation method, error correctionmethod, and the like. For example, as in FIG. 51, these pieces ofinformation can be transmitted to a communication partner by regulartransmission with only one modulated signal z1. It is also necessary totransmit symbols for estimation of channel fluctuation, i.e. for thereception device to estimate channel fluctuation (for example, a pilotsymbol, reference symbol, preamble, a Phase Shift Keying (PSK) symbolknown at the transmission and reception sides, and the like). In FIGS.47A, 47B, 48A, and 48B, these symbols are omitted. In practice, however,symbols for estimating channel fluctuation are included in the framestructure in the time and frequency domains. Accordingly, each carriergroup is not composed only of symbols for transmitting data. (The sameis true for Embodiment 1 as well.)

FIG. 52 is an example of the structure of a transmission device in abroadcast station (base station) according to the present embodiment. Atransmission method determining unit (5205) determines the number ofcarriers, modulation method, error correction method, coding ratio forerror correction coding, transmission method, and the like for eachcarrier group and outputs a control signal (5206).

A modulated signal generating unit #1 (5201_1) receives, as input,information (5200_1) and the control signal (5206) and, based on theinformation on the transmission method in the control signal (5206),outputs a modulated signal z1 (5202_1) and a modulated signal z2(5203_1) in the carrier group #A of FIGS. 47A, 47B, 48A, and 48B.

Similarly, a modulated signal generating unit #2 (5201_2) receives, asinput, information (5200_2) and the control signal (5206) and, based onthe information on the transmission method in the control signal (5206),outputs a modulated signal z1 (5202_2) and a modulated signal z2(5203_2) in the carrier group #B of FIGS. 47A, 47B, 48A, and 48B.

Similarly, a modulated signal generating unit #3 (5201_3) receives, asinput, information (5200_3) and the control signal (5206) and, based onthe information on the transmission method in the control signal (5206),outputs a modulated signal z1 (5202_3) and a modulated signal z2(5203_3) in the carrier group #C of FIGS. 47A, 47B, 48A, and 48B.

Similarly, a modulated signal generating unit #4 (5201_4) receives, asinput, information (5200_4) and the control signal (5206) and, based onthe information on the transmission method in the control signal (5206),outputs a modulated signal z1 (5202_4) and a modulated signal z2(5203_4) in the carrier group #D of FIGS. 47A, 47B, 48A, and 48B.

While not shown in the figures, the same is true for modulated signalgenerating unit #5 through modulated signal generating unit #M−1.

Similarly, a modulated signal generating unit #M (5201_M) receives, asinput, information (5200_M) and the control signal (5206) and, based onthe information on the transmission method in the control signal (5206),outputs a modulated signal z1 (5202_M) and a modulated signal z2(5203_M) in a certain carrier group.

An OFDM related processor (5207_1) receives, as inputs, the modulatedsignal z1 (5202_1) in carrier group #A, the modulated signal z1 (5202_2)in carrier group #B, the modulated signal z1 (5202_3) in carrier group#C, the modulated signal z1 (5202_4) in carrier group #D, . . . , themodulated signal z1 (5202_M) in a certain carrier group #M, and thecontrol signal (5206), performs processing such as reordering, inverseFourier transform, frequency conversion, amplification, and the like,and outputs a transmission signal (5208_1). The transmission signal(5208_1) is output as a radio wave from an antenna (5209_1).

Similarly, an OFDM related processor (5207_2) receives, as inputs, themodulated signal z1 (5203_1) in carrier group #A, the modulated signalz1 (5203_2) in carrier group #B, the modulated signal z1 (5203_3) incarrier group #C, the modulated signal z1 (5203_4) in carrier group #D,. . . , the modulated signal z1 (5203_M) in a certain carrier group #M,and the control signal (5206), performs processing such as reordering,inverse Fourier transform, frequency conversion, amplification, and thelike, and outputs a transmission signal (5208_2). The transmissionsignal (5208_2) is output as a radio wave from an antenna (5209_2).

FIG. 53 shows an example of a structure of the modulated signalgenerating units #1 #M in FIG. 52. An error correction encoder (5302)receives, as inputs, information (5300) and a control signal (5301) and,in accordance with the control signal (5301), sets the error correctioncoding method and the coding ratio for error correction coding, performserror correction coding, and outputs data (5303) after error correctioncoding. (In accordance with the setting of the error correction codingmethod and the coding ratio for error correction coding, when using LDPCcoding, turbo coding, or convolutional coding, for example, depending onthe coding ratio, puncturing may be performed to achieve the codingratio.)

An interleaver (5304) receives, as input, error correction coded data(5303) and the control signal (5301) and, in accordance with informationon the interleaving method included in the control signal (5301),reorders the error correction coded data (5303) and outputs interleaveddata (5305).

A mapper (5306_1) receives, as input, the interleaved data (5305) andthe control signal (5301) and, in accordance with the information on themodulation method included in the control signal (5301), performsmapping and outputs a baseband signal (5307_1).

Similarly, a mapper (5306_2) receives, as input, the interleaved data(5305) and the control signal (5301) and, in accordance with theinformation on the modulation method included in the control signal(5301), performs mapping and outputs a baseband signal (5307_2).

A signal processing unit (5308) receives, as input, the baseband signal(5307_1), the baseband signal (5307_2), and the control signal (5301)and, based on information on the transmission method (for example, inthis embodiment, a spatial multiplexing MIMO system, a MIMO method usinga fixed precoding matrix, a MIMO method for regularly hopping betweenprecoding matrices, space-time block coding, or a transmission methodfor transmitting only stream s1) included in the control signal (5301),performs signal processing. The signal processing unit (5308) outputs aprocessed signal z1 (5309_1) and a processed signal z2 (5309_2). Notethat when the transmission method for transmitting only stream s1 isselected, the signal processing unit (5308) does not output theprocessed signal z2 (5309_2). Furthermore, in FIG. 53, one errorcorrection encoder is shown, but the present invention is not limited inthis way. For example, as shown in FIG. 3, a plurality of encoders maybe provided.

FIG. 54 shows an example of the structure of the OFDM related processors(5207_1 and 5207_2) in FIG. 52. Elements that operate in a similar wayto FIG. 14 bear the same reference signs. A reordering unit (5402A)receives, as input, the modulated signal z1 (5400_1) in carrier group#A, the modulated signal z1 (5400_2) in carrier group #B, the modulatedsignal z1 (5400_3) in carrier group #C, the modulated signal z1 (5400_4)in carrier group #D, . . . , the modulated signal z1 (5400_M) in acertain carrier group, and a control signal (5403), performs reordering,and output reordered signals 1405A and 1405B. Note that in FIGS. 47A,47B, 48A, 48B, and 51, an example of allocation of the carrier groups isdescribed as being formed by groups of subcarriers, but the presentinvention is not limited in this way. Carrier groups may be formed bydiscrete subcarriers at each time interval. Furthermore, in FIGS. 47A,47B, 48A, 48B, and 51, an example has been described in which the numberof carriers in each carrier group does not change over time, but thepresent invention is not limited in this way. This point will bedescribed separately below.

FIGS. 55A and 55B show an example of frame structure in the time andfrequency domains for a method of setting the transmission method foreach carrier group, as in FIGS. 47A, 47B, 48A, 48B, and 51. In FIGS. 55Aand 55B, control information symbols are labeled 5500, individualcontrol information symbols are labeled 5501, data symbols are labeled5502, and pilot symbols are labeled 5503. Furthermore, FIG. 55A showsthe frame structure in the time and frequency domains for stream s1, andFIG. 55B shows the frame structure in the time and frequency domains forstream s2.

The control information symbols are for transmitting control informationshared by the carrier group and are composed of symbols for thetransmission and reception devices to perform frequency and timesynchronization, information regarding the allocation of (sub)carriers,and the like. The control information symbols are set to be transmittedfrom only stream s1 at time $1.

The individual control information symbols are for transmitting controlinformation on individual subcarrier groups and are composed ofinformation on the transmission method, modulation method, errorcorrection coding method, coding ratio for error correction coding,block size of error correction codes, and the like for the data symbols,information on the insertion method of pilot symbols, information on thetransmission power of pilot symbols, and the like. The individualcontrol information symbols are set to be transmitted from only streams1 at time $1.

The data symbols are for transmitting data (information), and asdescribed with reference to FIGS. 47A through 50, are symbols of one ofthe following transmission methods, for example: a spatial multiplexingMIMO system, a MIMO method using a fixed precoding matrix, a MIMO methodfor regularly hopping between precoding matrices, space-time blockcoding, or a transmission method for transmitting only stream s1. Notethat in carrier group #A, carrier group #B, carrier group #C, andcarrier group #D, data symbols are shown in stream s2, but when thetransmission method for transmitting only stream s1 is used, in somecases there are no data symbols in stream s2.

The pilot symbols are for the reception device to perform channelestimation, i.e. to estimate fluctuation corresponding to h₁₁(t),h₁₂(t), h₂₁(t), and h₂₂(t) in Equation 36. (In this embodiment, since amulti-carrier transmission method such as an OFDM method is used, thepilot symbols are for estimating fluctuation corresponding to h₁₁(t),h₁₂(t), h₂₁(t), and h₂₂(t) in each subcarrier.) Accordingly, the PSKtransmission method, for example, is used for the pilot symbols, whichare structured to form a pattern known by the transmission and receptiondevices. Furthermore, the reception device may use the pilot symbols forestimation of frequency offset, estimation of phase distortion, and timesynchronization.

FIG. 56 shows an example of the structure of a reception device forreceiving modulated signals transmitted by the transmission device inFIG. 52. Elements that operate in a similar way to FIG. 7 bear the samereference signs.

In FIG. 56, an OFDM related processor (5600_X) receives, as input, areceived signal 702_X, performs predetermined processing, and outputs aprocessed signal 704_X. Similarly, an OFDM related processor (5600_Y)receives, as input, a received signal 702_Y, performs predeterminedprocessing, and outputs a processed signal 704_Y.

The control information decoding unit 709 in FIG. 56 receives, as input,the processed signals 704_X and 704_Y, extracts the control informationsymbols and individual control information symbols in FIGS. 55A and 55Bto obtain the control information transmitted by these symbols, andoutputs a control signal 710 that includes the obtained information.

The channel fluctuation estimating unit 705_1 for the modulated signalz1 receives, as inputs, the processed signal 704_X and the controlsignal 710, performs channel estimation in the carrier group required bythe reception device (the desired carrier group), and outputs a channelestimation signal 706_1.

Similarly, the channel fluctuation estimating unit 705_2 for themodulated signal z2 receives, as inputs, the processed signal 704_X andthe control signal 710, performs channel estimation in the carrier grouprequired by the reception device (the desired carrier group), andoutputs a channel estimation signal 706_2.

Similarly, the channel fluctuation estimating unit 705_1 for themodulated signal z1 receives, as inputs, the processed signal 704_Y andthe control signal 710, performs channel estimation in the carrier grouprequired by the reception device (the desired carrier group), andoutputs a channel estimation signal 708_1.

Similarly, the channel fluctuation estimating unit 705_2 for themodulated signal z2 receives, as inputs, the processed signal 704_Y andthe control signal 710, performs channel estimation in the carrier grouprequired by the reception device (the desired carrier group), andoutputs a channel estimation signal 708_2.

The signal processing unit 711 receives, as inputs, the signals 706_1,706_2, 708_1, 708_2, 704_X, 704_Y, and the control signal 710. Based onthe information included in the control signal 710 on the transmissionmethod, modulation method, error correction coding method, coding ratiofor error correction coding, block size of error correction codes, andthe like for the data symbols transmitted in the desired carrier group,the signal processing unit 711 demodulates and decodes the data symbolsand outputs received data 712.

FIG. 57 shows the structure of the OFDM related processors (5600_X,5600_Y) in FIG. 56. A frequency converter (5701) receives, as input, areceived signal (5700), performs frequency conversion, and outputs afrequency converted signal (5702).

A Fourier transformer (5703) receives, as input, the frequency convertedsignal (5702), performs a Fourier transform, and outputs a Fouriertransformed signal (5704).

As described above, when using a multi-carrier transmission method suchas an OFDM method, carriers are divided into a plurality of carriergroups, and the transmission method is set for each carrier group,thereby allowing for the reception quality and transmission speed to beset for each carrier group, which yields the advantageous effect ofconstruction of a flexible system. In this case, as described in otherembodiments, allowing for choice of a method of regularly hoppingbetween precoding matrices offers the advantages of obtaining highreception quality, as well as high transmission speed, in an LOSenvironment. While in the present embodiment, the transmission methodsto which a carrier group can be set are “a spatial multiplexing MIMOsystem, a MIMO method using a fixed precoding matrix, a MIMO method forregularly hopping between precoding matrices, space-time block coding,or a transmission method for transmitting only stream s1”, but thetransmission methods are not limited in this way. Furthermore, thespace-time coding is not limited to the method described with referenceto FIG. 50, nor is the MIMO method using a fixed precoding matrixlimited to method #2 in FIG. 49, as any structure with a fixed precodingmatrix is acceptable. In the present embodiment, the case of twoantennas in the transmission device has been described, but when thenumber of antennas is larger than two as well, the same advantageouseffects may be achieved by allowing for selection of a transmissionmethod for each carrier group from among “a spatial multiplexing MIMOsystem, a MIMO method using a fixed precoding matrix, a MIMO method forregularly hopping between precoding matrices, space-time block coding,or a transmission method for transmitting only stream s1”.

FIGS. 58A and 58B show a method of allocation into carrier groups thatdiffers from FIGS. 47A, 47B, 48A, 48B, and 51. In FIGS. 47A, 47B, 48A,48B, 51, 55A, and 55B, carrier groups have described as being formed bygroups of subcarriers. In FIGS. 58A and 58B, on the other hand, thecarriers in a carrier group are arranged discretely. FIGS. 58A and 58Bshow an example of frame structure in the time and frequency domainsthat differs from FIGS. 47A, 47B, 48A, 48B, 51, 55A, and 55B. FIGS. 58Aand 58B show the frame structure for carriers 1 through H, times $1through $K. Elements that are similar to FIGS. 55A and 55B bear the samereference signs. Among the data symbols in FIGS. 58A and 58B, the “A”symbols are symbols in carrier group A, the “B” symbols are symbols incarrier group B, the “C” symbols are symbols in carrier group C, and the“D” symbols are symbols in carrier group D. The carrier groups can thusbe similarly implemented by discrete arrangement along (sub)carriers,and the same carrier need not always be used in the time domain. Thistype of arrangement yields the advantageous effect of obtaining time andfrequency diversity gain.

In FIGS. 47A, 47B, 48A, 48B, 51, 58A, and 58B, the control informationsymbols and the individual control information symbols are allocated tothe same time in each carrier group, but these symbols may be allocatedto different times. Furthermore, the number of (sub)carriers used by acarrier group may change over time.

Embodiment 16

Like Embodiment 10, the present embodiment describes a method forregularly hopping between precoding matrices using a unitary matrix whenN is an odd number.

In the method of regularly hopping between precoding matrices over aperiod (cycle) with 2N slots, the precoding matrices prepared for the 2Nslots are represented as follows.

$\begin{matrix}{{Equation}\mspace{14mu} 253} & \; \\{{{{{for}\mspace{14mu} i} = 0},1,2,\ldots\mspace{14mu},{N - 2},{N - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\mathbb{e}}^{j\;{\theta_{11}{({\mathbb{i}})}}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}}} \\{\alpha \times {\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}}} & {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \pi})}}\end{pmatrix}}}} & {{Math}\mspace{14mu} 294}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0.

$\begin{matrix}{{Equation}\mspace{14mu} 254} & \; \\{{{{{for}\mspace{14mu} i} = N},{N + 1},{N + 2},\ldots\mspace{14mu},{{2N} - 2},{{2N} - {1\text{:}}}}{{F\lbrack i\rbrack} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times {\mathbb{e}}^{{j\theta}_{11}{({\mathbb{i}})}}} & {\mathbb{e}}^{j{({{\theta_{11}{({\mathbb{i}})}} + \lambda})}} \\{\mathbb{e}}^{{j\theta}_{21}{({\mathbb{i}})}} & {\alpha \times {\mathbb{e}}^{j{({{\theta_{21}{({\mathbb{i}})}} + \lambda + \pi})}}}\end{pmatrix}}}} & {{Math}\mspace{14mu} 295}\end{matrix}$

Let α be a fixed value (not depending on i), where α>0. (Let the α inEquation 253 and the α in Equation 254 be the same value.)

From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment3, the following conditions are important in Equation 253 for achievingexcellent data reception quality.Math 296e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #46

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)Math 297e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=0,1,2, . . . ,N−2,N−1)  Condition #47

(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; andx≠y.)

Addition of the following condition is considered.Math 298θ₁₁(x)=θ₁₁(x+N) for ∀x(x=0,1,2, . . . ,N−2,N−1)andθ₂₁(y)=θ₂₁(y+N) for ∀y(y=0,1,2, . . . ,N−2,N−1)  Condition #48

Next, in order to distribute the poor reception points evenly withregards to phase in the complex plane, as described in Embodiment 6,Condition #49 and Condition #50 are provided.

$\begin{matrix}{{Condition}\mspace{14mu}{\# 49}} & \; \\{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}\;}} = {\mathbb{e}}^{j{(\frac{2\pi}{N})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Math}\mspace{14mu} 299} \\{{Condition}\mspace{14mu}{\# 50}} & \; \\{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\pi}{N}})}}}{{for}\mspace{14mu}{\forall{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Math}\mspace{14mu} 300}\end{matrix}$

$\begin{matrix}{{Math}\mspace{14mu} 300} & \; \\{{\frac{{\mathbb{e}}^{j{({{\theta_{11}{({x + 1})}} - {\theta_{21}{({x + 1})}}})}}}{{\mathbb{e}}^{j{({{\theta_{11}{(x)}} - {\theta_{21}{(x)}}})}}} = {\mathbb{e}}^{j{({- \frac{2\;\pi}{N}})}}}\mspace{14mu}{{for}\mspace{14mu}{\forall\;{x\left( {{x = 0},1,2,\ldots\mspace{14mu},{N - 2}} \right)}}}} & {{Condition}\mspace{14mu}{\# 50}}\end{matrix}$

In other words, Condition #49 means that the difference in phase is 2π/Nradians. On the other hand, Condition #50 means that the difference inphase is −2π/N radians.

Letting θ₁₁(0)−θ₂₁(0)=0 radians, and letting α>1, the distribution ofpoor reception points for s1 and for s2 in the complex plane for N=3 isshown in FIGS. 60A and 60B. As is clear from FIGS. 60A and 60B, in thecomplex plane, the minimum distance between poor reception points for s1is kept large, and similarly, the minimum distance between poorreception points for s2 is also kept large. Similar conditions arecreated when α<1. Furthermore, upon comparison with FIGS. 45A and 45B inEmbodiment 10, making the same considerations as in Embodiment 9, theprobability of a greater distance between poor reception points in thecomplex plane increases when N is an odd number as compared to when N isan even number. However, when N is small, for example when N≦16, theminimum distance between poor reception points in the complex plane canbe guaranteed to be a certain length, since the number of poor receptionpoints is small. Accordingly, when N≦16, even if N is an even number,cases do exist where data reception quality can be guaranteed.

Therefore, in the method for regularly hopping between precodingmatrices based on Equations 253 and 254, when N is set to an odd number,the probability of improving data reception quality is high. Precodingmatrices F[0]−F[2N−1] are generated based on Equations 253 and 254 (theprecoding matrices F[0]−F[2N−1] may be in any order for the 2N slots inthe period (cycle)). Symbol number 2Ni may be precoded using F[0],symbol number 2Ni+1 may be precoded using F[1], . . . , and symbolnumber 2N×i+h may be precoded using F[h], for example (h=0, 1, 2, . . ., 2N−2, 2N−1). (In this case, as described in previous embodiments,precoding matrices need not be hopped between regularly.) Furthermore,when the modulation method for both s1 and s2 is 16QAM, if a is set asin Equation 233, the advantageous effect of increasing the minimumdistance between 16×16=256 signal points in the IQ plane for a specificLOS environment may be achieved.

The following conditions are possible as conditions differing fromCondition #48:Math 301e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x))) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y))) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)  Condition #51

(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . ,2N−2, 2N−1; and x y.)Math 302e ^(j(θ) ¹¹ ^((x)−θ) ²¹ ^((x)−π)) ≠e ^(j(θ) ¹¹ ^((y)−θ) ²¹ ^((y)−π)) for∀x,∀y(x≠y;x,y=N,N+1,N+2, . . . ,2N−2,2N−1)  Condition #52

(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . ,2N−2, 2N−1; and x y.)

In this case, by satisfying Condition #46, Condition #47, Condition #51,and Condition #52, the distance in the complex plane between poorreception points for s1 is increased, as is the distance between poorreception points for s2, thereby achieving excellent data receptionquality.

In the present embodiment, the method of structuring 2N differentprecoding matrices for a precoding hopping method with a 2N-slot timeperiod (cycle) has been described. In this case, as the 2N differentprecoding matrices, F[0], F[1], F[2], F[2N−2], F[2N−1] are prepared. Inthe present embodiment, an example of a single carrier transmissionmethod has been described, and therefore the case of arranging symbolsin the order F[0], F[1], F[2], F[2N−2], F[2N−1] in the time domain (orthe frequency domain) has been described. The present invention is not,however, limited in this way, and the 2N different precoding matricesF[0], F[1], F[2], F[2N−2], F[2N−1] generated in the present embodimentmay be adapted to a multi-carrier transmission method such as an OFDMtransmission method or the like. As in Embodiment 1, as a method ofadaption in this case, precoding weights may be changed by arrangingsymbols in the frequency domain and in the frequency-time domain. Notethat a precoding hopping method with a 2N-slot time period (cycle) hasbeen described, but the same advantageous effects may be obtained byrandomly using 2N different precoding matrices. In other words, the 2Ndifferent precoding matrices do not necessarily need to be used in aregular period (cycle).

Furthermore, in the precoding matrix hopping method over an H-slotperiod (cycle) (H being a natural number larger than the number of slots2N in the period (cycle) of the above method of regularly hoppingbetween precoding matrices), when the 2N different precoding matrices ofthe present embodiment are included, the probability of excellentreception quality increases.

Embodiment 17

Embodiment 17 describes an arrangement of precoded symbols that achieveshigh reception quality in a transmission method for a MIMO system forregularly hopping between precoding matrices.

FIGS. 61A and 61B show an example of the frame structure of a portion ofthe symbols in a signal in the time-frequency domains when using amulti-carrier method, such as an OFDM method, in the transmission methodthat regularly hops between precoding matrices. FIG. 61A shows the framestructure of a modulated signal z1, and FIG. 61B shows the framestructure of a modulated signal z2. In both of these figures, one squarerepresents one symbol.

In modulated symbol z1 and modulated symbol z2 of FIG. 61A and FIG. 61B,symbols that are allocated to the same carrier number are transmitted bya plurality of antennas of the transmission device at the same time overthe same frequency.

The following focuses on symbol 610 a in carrier f2 and at time t2 ofFIG. 61A. Note that while the term “carrier” is used here, the term“subcarrier” may also be used.

In carrier f2, an extremely high correlation exists between the channelconditions of the closest symbols in terms of time to time t2, i.e.symbol 613 a at time t1 and symbol 611 a at time t3 in carrier f2, andthe channel conditions of symbol 610 a at time t2 in carrier f2.

Similarly, at time t2, an extremely high correlation exists between thechannel conditions of the symbols at the closest frequencies to carrierf2 in the frequency domain, i.e. symbol 612 a at time t2 in carrier f1and symbol 614 a at time t2 in carrier f3, and the channel conditions ofsymbol 610 a at time t2 in carrier f2.

As described above, an extremely high correlation exists between thechannel conditions of symbols 611 a, 612 a, 613 a, and 614 a and thechannel conditions of symbol 610 a.

Note that the same correlations of course exist for symbols 610 b-614 bof modulated signal z2.

In the present description, N types of matrices (where N is an integerequal to or greater than five) are used as the precoding matrices in thetransmission method that regularly hops between precoding matrices. Thesymbols shown in FIGS. 61A and 61B bear labels such as “#1”, forexample, which indicates that the symbol has been precoded withprecoding matrix #1. In other words, precoding matrices #1 #N areprepared. Accordingly, the symbol bearing the label “#N” has beenprecoded with precoding matrix #N.

The present embodiment discloses utilization of the high correlationbetween the channel conditions of symbols that are adjacent in thefrequency domain and symbols that are adjacent in the time domain in anarrangement of precoded symbols that yields high reception quality atthe reception device.

The condition (referred to as Condition #53) for obtaining highreception quality at the reception side is as follows.

Condition #53

In a transmission method that regularly hops between precoding matrices,when using a multi-carrier transmission method such as OFDM, thefollowing five symbols for data transmission (hereinafter referred to asdata symbols) are each precoded with a different precoding matrix: thedata symbol at time X in carrier Y; the symbols that are adjacent in thetime domain, namely the data symbols at time X−1 in carrier Y and attime X+1 in carrier Y; and the symbols that are adjacent in thefrequency domain, namely the data symbols at time X in carrier Y−1 andat time X in carrier Y+1.

The reason behind Condition #53 is as follows. For a given symbol in thetransmission signal (hereinafter referred to as symbol A), a highcorrelation exists between (i) the channel conditions of symbol A and(ii) the channel conditions of the symbols adjacent to symbol A in termsof time and the symbols adjacent to symbol A in terms of frequency, asdescribed above.

By using different precoding matrices for these five symbols, in an LOSenvironment, even if the reception quality of symbol A is poor (althoughthe reception quality is high in terms of SNR, the condition of thephase relationship of the direct waves is poor, causing poor receptionquality), the probability of excellent reception quality in theremaining four symbols adjacent to symbol A is extremely high.Therefore, after error correction decoding, excellent reception qualityis obtained.

On the other hand, if the same precoding matrix as symbol A is used forthe symbols adjacent to symbol A in terms of time or adjacent in termsof frequency, the symbols precoded with the same precoding matrix havean extremely high probability of poor reception quality like symbol A.Therefore, after error correction decoding, the data reception qualitydegrades.

FIGS. 61A and 61B show an example of symbol arrangement for obtainingthis high reception quality, whereas FIGS. 62A and 62B show an exampleof symbol arrangement in which reception quality degrades.

As is clear from FIG. 61A, the precoding matrix used for symbol 610 a,which corresponds to symbol A, the precoding matrices used for symbols611 a and 613 a, which are adjacent in terms of time to symbol 610 a,and the precoding matrices used for symbols 612 a and 614 a, which areadjacent in terms of frequency to symbol 610 a, are chosen to all differfrom each other. In this way, even if the reception quality of symbol610 a is poor at the receiving end, the reception quality of theadjacent symbols is extremely high, thus guaranteeing high receptionquality after error correction decoding. Note that the same can be saidfor the modulated signal z2 in FIG. 61B.

On the other hand, as is clear from FIG. 62A, the precoding matrix usedfor symbol 620 a, which corresponds to symbol A, and the precodingmatrix used for symbol 624 a, which is adjacent to symbol A in terms offrequency, are the same precoding matrix. In this case, if the receptionquality for symbol 620 a at the receiving end is poor, the probabilityis high that the reception quality for symbol 624 a, which used the sameprecoding matrix, is also poor, causing reception quality after errorcorrection decoding to degrade. Note that the same can be said for themodulated signal z2 in FIG. 62B.

Therefore, in order for the reception device to achieve excellent datareception quality, it is important for symbols that satisfy Condition#53 to exist. In order to improve the data reception quality, it istherefore preferable that many data symbols satisfy Condition #53.

The following describes a method of allocating precoding matrices tosymbols that satisfy Condition #53.

Based on the above considerations, the following shows a method ofallocating symbols so that all of the data symbols satisfy the symbolallocation shown in FIGS. 61A and 61B. One important condition (methodof structuring) is the following Condition #54.

Condition #54

Five or more precoding matrices are necessary. As shown in FIGS. 61A and61B, at least the precoding matrices that are multiplied with the fivesymbols arranged in the shape of a cross are necessary. In other words,the number N of different precoding matrices that satisfy Condition #53must be five or greater. Stated another way, the period (cycle) ofprecoding matrices must have at least five slots.

When this condition is satisfied, it is possible to arrange symbolssatisfying Condition #53 by allocating precoding matrices based on thefollowing method and then precoding symbols.

First, in the frequency bandwidth that is to be used, one of N precodingmatrices is allocated to the smallest carrier number and the smallesttime (the earliest time from the start of transmission). As an example,in FIG. 63A, precoding matrix #1 is allocated to carrier f1, time t1. Inthe frequency domain, the index of the precoding matrix used forprecoding is then changed one at a time (i.e. incremented). Note thatthe “index” in this context is used to distinguish between precodingmatrices. In the method of regularly hopping between precoding matrices,a period (cycle) exists, and the precoding matrices that are used arearranged cyclically. In other words, focusing on time t1 in FIG. 63A,since the precoding matrix with index #1 is used in carrier f1, theprecoding matrix with index #2 is used in carrier f2, the precodingmatrix with index #3 is used in carrier f3, the precoding matrix withindex #4 is used in carrier f4, the precoding matrix with index #5 isused in carrier f5, the precoding matrix with index #1 is used incarrier f6, the precoding matrix with index #2 is used in carrier f7,the precoding matrix with index #3 is used in carrier f8, the precodingmatrix with index #4 is used in carrier f9, the precoding matrix withindex #5 is used in carrier f10, the precoding matrix with index #1 isused in carrier f11, and so forth.

Next, using the smallest carrier number as a reference, the index of theprecoding matrix allocated to the smallest carrier number (i.e. #X) isshifted in the time domain by a predetermined number (hereinafter, thispredetermined number is indicated as Sc). Shifting is synonymous withincreasing the index by Sc. At times other than the smallest time, theindex of the precoding matrix used for precoding is changed(incremented) in the frequency domain according to the same rule as forthe smallest time. In this context, when numbers from 1 to N areassigned to the prepared precoding matrices, shifting refers toallocating precoding matrices with numbers that are incremented withrespect to the numbers of the precoding matrices allocated to theprevious time slot in the time domain.

For example, focusing on time t2 in FIG. 63A, the precoding matrix withindex #4 is allocated to carrier f1, the precoding matrix with index #5to carrier f2, the precoding matrix with index #1 to carrier f3, theprecoding matrix with index #2 to carrier f4, the precoding matrix withindex #3 to carrier f5, the precoding matrix with index #4 to carrierf6, the precoding matrix with index #5 to carrier f7, the precodingmatrix with index #1 to carrier f8, the precoding matrix with index #2to carrier f9, the precoding matrix with index #3 to carrier f10, theprecoding matrix with index #4 to carrier f11, and so forth.Accordingly, different precoding matrices are used in the same carrierat time t1 and time t2.

In order to satisfy Condition #53, the value of Sc for shifting theprecoding matrices in the time domain is given by Condition #55.

Condition #55

Sc is between two and N−2, inclusive.

In other words, when precoding matrix #1 is allocated to the symbol incarrier f1 at time t1, the precoding matrices allocated in the timedomain are shifted by Sc. That is, the symbol in carrier f1 at time t2has the precoding matrix indicated by the number 1+Sc allocated thereto,the symbol in carrier f1 at time t3 has the precoding matrix indicatedby the number 1+Sc+Sc allocated thereto, . . . , the symbol in carrierf1 at time tn has allocated thereto the precoding matrix indicated bySc+(the number of the precoding matrix allocated to the symbol at timetn−1), and so forth. Note that when the value obtained by additionexceeds the prepared number N of different precoding matrices, N issubtracted from the value obtained by addition to yield the precodingmatrix that is used. Specifically, letting N be five, Sc be two, andprecoding matrix #1 be allocated to the smallest carrier f1 at time t1,the precoding matrix in carrier f1 at time t2 is precoding matrix #3(1+2(Sc)), the precoding matrix in carrier f1 at time t3 is precodingmatrix #5 (3+2(Sc)), the precoding matrix in carrier f1 at time t4 isprecoding matrix #2 (5+2(Sc)−5(N)), and so forth.

Once the precoding matrices allocated to each time tx for the smallestcarrier number are determined, the precoding matrices allocated in thesmallest carrier number at each time are incremented to allocatesubsequent precoding matrices. For example, in FIG. 63A, when theprecoding matrix used for the symbol in carrier f1 at time t1 isprecoding matrix #1, then the precoding matrices that symbols aremultiplied by are allocated as follows: the precoding matrix used forthe symbol in carrier f2 at time t1 is precoding matrix #2, theprecoding matrix used for the symbol in carrier f3 at time t1 isprecoding matrix #3, . . . . Note that in the frequency domain as well,when the number allocated to the precoding matrix reaches N, the numberreturns to one, thus forming a loop.

FIGS. 63A and 63B thus show an example of symbol arrangement for datasymbols precoded with the precoding matrix allocated thereto. For themodulated signal z1 shown in FIG. 63A and the modulated signal z2 shownin FIG. 63B, an example of symbol arrangement is shown in which fiveprecoding matrices are prepared, and three is used as the aboveincremental value Sc.

As is clear from FIGS. 63A and 63B, data symbols are arranged afterbeing precoded using precoding matrices whose numbers are shifted inaccordance with the above method. As is also clear from FIGS. 63A and63B, in this arrangement the above Condition #53 is satisfied, sincewhen focusing on a data symbol in any position, the precoding matrixused for the data symbol and the precoding matrices used for the datasymbols that are adjacent thereto in the frequency and time domains areall different. However, in the case of a data symbol A for which thereare three or fewer data symbols adjacent thereto in the frequency andtime domains, the number of adjacent data symbols being X (where X isequal to or less than three), then different precoding matrices are usedfor the X adjacent data symbols and the data symbol A. For example, inFIG. 63A, the data symbol at f1, t1 only has two adjacent data symbols,the data symbol at f1, t2 only has three adjacent data symbols, and thedata symbol at f2, t1 only has three adjacent data symbols. For each ofthese data symbols as well, however, different precoding matrices areallocated to the data symbol and the adjacent data symbols.

Furthermore, it is clear that the index of precoding matrices isincreased by a value of three for Sc, since the difference between theindex of the precoding matrix used for symbol 631 a and the precodingmatrix used for symbol 630 a in FIG. 63A is 4−1=3, and the differencebetween the index of the precoding matrix used for symbol 632 a and theprecoding matrix used for symbol 631 a in FIG. 63A is 2+5−4=3. Thisvalue of Sc is within the range 2≦Sc≦3(5(N)−2), thus satisfyingCondition #55.

FIGS. 64A and 64B show an example of symbol arrangement with fiveprecoding matrices and two as the above incremental value Sc.

In the transmission device, as an example of the method for achievingthis symbol arrangement, the precoding matrix with the smallest number(precoding matrix #1 in FIGS. 63A and 63B) is allocated as the precodingmatrix used for the symbol in the smallest carrier (for example, carrierf1 in FIGS. 63A and 63B) when precoding the data symbols. The number ofthe precoding matrix allocated to the smallest carrier, precoding matrix#1, is then shifted in the time domain by the predetermined number Sc inorder to allocate precoding matrices. For this method, a registerindicating the predetermined value of Sc is provided, and the value setin the register is added to the number of the allocated precodingmatrix.

After allocating precoding matrices to the smallest carrier for thenecessary number of time slots, the precoding matrix allocated to eachtime slot should be incremented one at a time in the frequency domainuntil reaching the largest carrier that is used.

In other words, a structure should be adopted in which the number of theprecoding matrices used in the frequency domain is incremented one at atime, whereas the number of the precoding matrices used in the timedomain is shifted by Sc.

For the modulated signal z1 shown in FIGS. 63A and 64A and the modulatedsignal z2 shown in FIGS. 63B and 64B, symbols are arranged after beingprecoded using precoding matrices whose numbers are shifted inaccordance with the above method, and it is clear that when focusing onany of the symbols, Condition #53 is satisfied.

By transmitting signals generated in this way, at the reception device,even if the reception quality of a certain symbol is poor, it is assumedthat the reception quality of symbols that are adjacent in the frequencyand time domains will be higher. Therefore, after error correctiondecoding, excellent reception quality is guaranteed.

In the above-described allocation method of precoding matrices, thesmallest carrier is determined, and precoding matrices are shifted by Scin the time domain, but precoding matrices may be shifted by Sc in thefrequency domain. In other words, after determining the precoding matrixallocated to the earliest time t1 in carrier f1, precoding matrices maybe allocated by shifting the precoding matrix by Sc one carrier at atime in the frequency domain. In the same carrier, the index of eachprecoding matrix would then be incremented one at a time in the timedomain. In this case, the symbol arrangements shown in FIGS. 63A, 63B,64A, and 64B would become the symbol arrangements shown in FIGS. 65A,65B, 66A, and 66B.

As shown in FIGS. 67A through 67D, a variety of methods exist for theorder of incrementing the index of the precoding matrix, and any ofthese orders may be used. In FIGS. 67A through 67D, the index of theprecoding matrices is incremented in the order of the numbers 1, 2, 3,4, . . . assigned to the arrows.

FIG. 67A shows a method in which, as shown in FIGS. 63A, 63B, 64A, and64B, the index of the precoding matrices used at time A is incrementedin the frequency domain; when finished, the index of the precodingmatrices used at time A+1 is incremented in the frequency domain; and soforth.

FIG. 67B shows a method in which, as described in FIGS. 63A, 63B, 64A,and 64B, the index of the precoding matrices used at frequency A isincremented in the time domain; when finished, the index of theprecoding matrices used at frequency A+1 is incremented in the timedomain; and so forth.

FIGS. 67B and 67D are modifications of FIGS. 67A and 67C respectively.The index of the precoding matrices that are used is incremented in thefollowing way. First, the index of the precoding matrices used for thesymbols indicated by arrow 1 is incremented in the direction of thearrow. When finished, the index of the precoding matrices used for thesymbols indicated by arrow 2 is incremented in the direction of thearrow, and so forth.

For a method other than the methods shown in FIGS. 67A through 67D, itis preferable to implement a precoding method that results in many datasymbols satisfying Condition #53, as in FIGS. 63A through 66B.

Note that precoding matrices may be incremented in accordance with amethod other than the methods of incrementing the index of precodingmatrices shown in FIGS. 67A through 67D, in which case a method yieldingmany data symbols satisfying Condition #53 is preferable.

Modulated signals generated in this way are transmitted from a pluralityof antennas in the transmission device.

This concludes the example of arrangement of precoded symbols accordingto Embodiment 17 for reducing degradation of reception quality at thereceiving end.

Note that in Embodiment 17, methods have been shown in which many datasymbols satisfy Condition #53 by using, in symbols adjacent to a certainsymbol, precoding matrices whose number has been shifted by apredetermined number from the precoding matrix for the certain symbol.However, as long as data symbols satisfying Condition #53 exist, theadvantageous effect of improved data reception quality can be achievedeven without allocating precoding matrices regularly as shown inEmbodiment 17.

Furthermore, in the method of the present embodiment, treating thesymbol to which a precoding matrix is first allocated as a reference,precoding matrix #1 is allocated to the symbol in the smallest carrier,and the precoding matrices are shifted by one or by Sc in the frequencyand time domains, but this method may be adapted to allocate precodingmatrices starting from the largest carrier. Alternatively, a structuremay be adopted whereby precoding matrix #N is allocated to the smallestcarrier, and the precoding matrices are then shifted by subtraction. Inother words, the index numbers of different precoding matrices inEmbodiment 17 are only an example, and as long as many data symbolssatisfy Condition #53, any index numbers may be assigned.

Information indicating the allocation method of precoding matrices shownin Embodiment 17 is generated by the weighting information generatingunit 314 shown in Embodiment 1, and in accordance with the generatedinformation, the weighting units 308A and 308B or the like performprecoding.

Additionally, while in the method of regularly hopping between precodingmatrices, the number of precoding matrices used does not change (i.e.,different precoding matrices F[0], F[1], . . . , F[N−1] are prepared,and the precoding matrices F[0], F[1], . . . , F[N−1] are hopped betweenand used), it is possible to switch between the method of allocatingprecoding matrices of the present embodiment and of other embodiments inunits of frames, in units of symbol blocks composed of complex symbols,and the like. In this case, the transmission device transmitsinformation regarding the method of allocating precoding matrices. Byreceiving this information, the reception device learns the method ofallocating precoding matrices, and based on the method, decodes theprecoded symbols. Predetermined methods of allocating the precodingmatrices exist, such as allocation method A, allocation method B,allocation method C, and allocation method D. The transmission deviceselects an allocation method from among A-D and transmits information tothe reception device to indicate which of the methods A-D is used. Byacquiring this information, the reception device is able to decode theprecoded symbols.

Note that in the present embodiment, the case of transmitting modulatedsignals s1, s2 and z1, z2 has been described, i.e. an example of twostreams and two transmission signals. The number of streams and oftransmission signals is not limited in this way, however, and precodingmatrices may be similarly allocated when the number is larger than two.In other words, if streams of modulated signals s3, s4, . . . exist, andtransmission signals for the modulated signals z3, z4, . . . exist, thenin z3 and z4, the index of the precoding matrices for the symbols inframes in the frequency-time domains may be changed similarly to z1 andz2.

Embodiment 18

In Embodiment 17, conditions when allocating only data symbols have beendescribed. In practice, however, pilot symbols and symbols fortransmitting control information can also be thought to exist. (Whilethe term “pilot symbol” is used here, an appropriate example is a knownPSK modulation symbol that does not transmit data, and a name such as“reference symbol” may be used. Typically, this symbol is used forestimation of channel conditions, estimation of frequency offset amount,acquisition of time synchronization, signal detection, estimation ofphase distortion, and the like.) Therefore, Embodiment 18 describes amethod of allocating precoding matrices for data symbols among whichpilot symbols are inserted.

In Embodiment 17, FIGS. 63A, 63B, 64A, 64B, 65A, 65B, 66A, and 66B showan example in which no pilot symbols or symbols for transmitting controlinformation are allocated at the time when data symbols are allocated.In this case, letting the starting time at which data symbols areallocated be t1, pilot symbols or symbols for transmitting controlinformation may be allocated before t1 (in this case, such symbols maybe referred to as a preamble). Furthermore, in order to improve datareception quality in the reception device, pilot symbols may beallocated at the time after the last time at which data symbols areallocated (see FIG. 68A). Note that FIG. 68A shows the case in whichpilot symbols (P) occur, but as described above, these pilot symbols (P)may be replaced by symbols (C) for transmitting control information.

Furthermore, pilot symbols or symbols for transmitting controlinformation, which are not data symbols, may be allocated to a specificcarrier. As an example, FIG. 68B shows arrangement of pilot symbols inthe carriers at either end of the frequency domain. Even with thisarrangement, many data symbols satisfying Condition #53 may be providedas in Embodiment 17. Furthermore, it is not necessary as in FIG. 68B forpilot symbols to be arranged at either end of the frequencies used fordata symbols in the frequency domain. For example, pilot symbols (P) maybe arranged in a specific carrier as in FIG. 68C, or instead of pilotsymbols, control information (C) may be arranged in a specific carrier,as in FIG. 68D. Even with the arrangements in FIGS. 68C and 68D, manydata symbols satisfying Condition #53 may be provided as in Embodiment17. Note that in FIGS. 68A through 68D, no difference is made betweenmodulated signals, since this description holds for both modulatedsignals z1 and z2.

In other words, even if symbols that are not data symbols, such as pilotsymbols or symbols for transmitting control information, are arranged inspecific carriers, many data symbols satisfying Condition #53 may beprovided. Furthermore, as described above, in FIGS. 68A through 68D,even if symbols that are not data symbols, such as pilot symbols orsymbols for transmitting control information, are arranged before thetime when data symbols are first arranged, i.e. before time t1, manydata symbols satisfying Condition #53 may be provided.

Additionally, even if only symbols other than data symbols are arrangedat a specific time instead of data symbols, many data symbols satisfyingCondition #53 may be provided.

Note that in FIGS. 68A through 68D, the case of pilot symbols in bothmodulated signals z1 and z2 at the same time and in the same carrier hasbeen described, but the present invention is not limited in this way.For example, a structure may be adopted in which a pilot symbol isprovided in modulated signal z1 whereas a symbol with in-phasecomponents I of zero and quadrature components Q of zero is provided inmodulated signal z2. Conversely, a structure may be adopted in which asymbol with in-phase components I of zero and quadrature components Q ofzero is provided in modulated signal z1, whereas a pilot symbol isprovided in modulated signal z2.

In the frames in the time-frequency domains described so far, a framestructure in which symbols other than data symbols only occur atspecified times or in specified carriers has been described. As anexample differing from these examples, the following describes the casein which the subcarrier including a pilot symbol P changes over time, asshown in FIGS. 69A and 69B. In particular, the following describes amethod of allocating precoding matrices so that precoded data symbolsthat are located in the positions shown in FIGS. 69A and 69B (thesquares not labeled P) satisfy Condition #53 of Embodiment 17. Notethat, as in the above description, the case of pilot symbols in bothmodulated signals z1 and z2 at the same time and in the same carrier isdescribed, but the present invention is not limited in this way. Forexample, a structure may be adopted in which a pilot symbol is providedin modulated signal z1 whereas a symbol with in-phase components I ofzero and quadrature components Q of zero is provided in modulated signalz2. Conversely, a structure may be adopted in which a symbol within-phase components I of zero and quadrature components Q of zero isprovided in modulated signal z1, whereas a pilot symbol is provided inmodulated signal z2.

First, when the index of the precoding matrix that is used is simplyincremented as described in Embodiment 17, one possibility is not toincrement the index of the precoding matrix for symbols other than datasymbols. FIGS. 70A and 70B show an example of symbol arrangement in thiscase. In FIGS. 70A and 70B, as in FIG. 67A, the method is adoptedwhereby the index of precoding matrices is incremented in the frequencydomain and is shifted by Sc in the time domain. In this case, when theindex of the precoding matrices is incremented in the frequency domain,for symbols other than data symbols, the index of the precoding matrixis not incremented. Adopting this structure in the method of regularlyhopping between precoding matrices offers the advantage of maintaining aconstant period (cycle) and of providing data symbols that satisfyCondition #53.

In particular, when the following conditions are satisfied, many datasymbols satisfying Condition #53 can be provided.

<a> In time slots i−1, i, and i+1, in which data symbols exist, lettingthe number of pilot symbols existing at time i−1 be A, the number ofpilot symbols existing at time i be B, and the number of pilot symbolsexisting at time i+1 be C, the difference between A and B is 0 or 1, thedifference between B and C is 0 or 1, and the difference between A and Cis 0 or 1.

Condition <a> may also be expressed as follows.

<a′> In time slots i−1, i, and i+1, in which data symbols exist, lettingthe number of data symbols existing at time i−1 be a, the number of datasymbols existing at time i be β, and the number of data symbols existingat time i+1 be γ, the difference between α and β is 0 or 1, thedifference between 13 and γ is 0 or 1, and the difference between α andy is 0 or 1.

Relaxing the conditions in conditions <a> and <a′> yields the following.

<b> In time slots i−1, i, and i+1, in which data symbols exist, lettingthe number of pilot symbols existing at time i−1 be A, the number ofpilot symbols existing at time i be B, and the number of pilot symbolsexisting at time i+1 be C, the difference between A and B is 0, 1, or 2,the difference between B and C is 0, 1, or 2, and the difference betweenA and C is 0, 1, or 2.<b′> In time slots i−1, i, and i+1, in which data symbols exist, lettingthe number of data symbols existing at time i−1 be a, the number of datasymbols existing at time i be β, and the number of data symbols existingat time i+1 be γ, the difference between α and β is 0, 1, or 2, thedifference between β and γ is 0, 1, or 2, and the difference between αand γ is 0, 1, or 2.

It is preferable to use a large period (cycle) in the method ofregularly hopping between precoding matrices, and for the value of Sc tobe “equal to or greater than X and less than or equal to N−X, where X islarge”.

With these conditions, selecting any two of (i) the number of times theindex of the precoding matrices is incremented at time i−1, (ii) thenumber of times the index of the precoding matrices is incremented attime i, and (iii) the number of times the index of the precodingmatrices is incremented at time i+1, the difference therebetween is atmost one. Therefore, the probability of maintaining the conditionsdescribed in Embodiment 17 is high.

Focusing on symbol 700 a in FIG. 70A, however, indicates that this datasymbol does not satisfy Condition #53, which requires that the precodingmatrix used in symbol 700 a and the precoding matrices used in thesymbols adjacent to symbol 700 a in the frequency and time domains allbe different. A small number of data symbols like symbol 700 a do exist.(In FIG. 70A, the reason many data symbols satisfy Condition #53 is thatthe above conditions are satisfied. Furthermore, depending on the methodof allocation, it is possible for all data symbols having adjacent datasymbols to satisfy Condition #53. Embodiment 20 shows an example suchallocation.)

Another method is to increment the index number of precoding matriceseven at locations where pilot symbols are inserted.

FIGS. 71A and 71B show a method of allocating precoding matrices whenthe pilot symbols of the present embodiment are inserted in the exampleof the method of allocating precoding matrices for data symbols shown inFIGS. 63A and 63B.

As shown in FIGS. 71A and 71B, at each location where a pilot symbol isallocated, a data symbol is assumed to exist for the purpose ofallocating a precoding matrix. In other words, precoding matrices areallocated as in Embodiment 17, resulting in deletion of the number ofthe precoding matrix used at a position where a pilot symbol is located.

This arrangement offers the advantageous effect that all of the datasymbols in the time and frequency domains satisfy Condition #53.However, since pilot symbols are inserted, the period (cycle) in themethod of regularly hopping between precoding matrices is no longerconstant.

Information indicating the allocation method of precoding matrices shownin Embodiment 18 may be generated by the weighting informationgenerating unit 314 shown in Embodiment 1, and in accordance with thegenerated information, the weighting units 308A and 308B or the like mayperform precoding and transmit information corresponding to the aboveinformation to the communication partner. (This information need not betransmitted when a rule is predetermined, i.e. when the method ofallocating precoding matrices is determined in advance at thetransmission side and the reception side.) The communication partnerlearns of the allocation method of precoding matrices used by thetransmission device and, based on this knowledge, decodes precodedsymbols.

In the present embodiment, the case of transmitting modulated signalss1, s2 and modulated signals z1, z2 has been described, i.e. an exampleof two streams and two transmission signals. The number of streams andof transmission signals is not limited in this way, however, and maysimilarly be implemented by allocating precoding matrices when thenumber is larger than two. In other words, if streams of modulatedsignals s3, s4, . . . exist, and transmission signals z3, z4, . . .exist, then in z3 and z4, the index of the precoding matrices for thesymbols in frames in the frequency-time domains may be allocatedsimilarly to the modulated signals z1 and z2.

Embodiment 19

Embodiment 17 and Embodiment 18 describe an example focusing on fivedata symbols, namely a certain data symbol and the symbols that areclosest to the certain data symbol in terms of time and frequency,wherein the precoding matrices assigned to the five data symbols are alldifferent. Embodiment 19 describes a method for allocating precodingmatrices that expands the range over which precoding matrices used fornearby data symbols differ from each other. Note that in the presentembodiment, a range over which precoding matrices allocated to all ofthe symbols in the range differ is referred to as a “differing range”for the sake of convenience.

In Embodiments 17 and 18, precoding matrices are allocated so that, forfive data symbols in the shape of a cross, the precoding matrices usedfor the data symbols differ from each other. In this embodiment,however, the range over which precoding matrices that differ from eachother are allocated to data symbols is expanded, for example to threesymbols in the direction of frequency and three symbols in the timedomain, for a total of 3×3=9 data symbols. Precoding matrices thatdiffer from each other are allocated to these nine data symbols. Withthis method, the data reception quality at the reception side may behigher than the symbol arrangement shown in Embodiment 17 in which onlyfive symbols are multiplied by different precoding matrices. (Asmentioned above, the present embodiment describes the case of expansionto M symbols in the time domain and N symbols in the frequency domain,i.e. N×M data symbols.) The following describes a method of allocatingprecoding matrices by describing this expansion, and subsequently,conditions for achieving the expansion.

FIGS. 72A through 78B show examples of frame structure and of expandedarrangements of symbols multiplied by mutually different precodingmatrices.

FIGS. 72A, 72B, 73A, and 73B show examples of frame structure of amodulated signal with a differing range of 3×3. FIGS. 75A and 75B showexpansion of the differing range to 3×5. FIGS. 77A and 77B show anexample of a diamond-like range.

First, in the rectangular differing ranges shown in FIGS. 72A, 72B, 73A,73B, 75A, and 75B, the minimum necessary number of different precodingmatrices equals the number of symbols included in the differing range.In other words, the minimum number of different precoding matrices isthe product of the number of symbols in the frequency domain and thenumber of symbols in the time domain in the differing range. (As shownin FIGS. 73A and 73B, a larger number of different precoding matricesthan the minimum number may be prepared.) That is, letting the period(cycle) for hopping in the method of regularly hopping between precodingmatrices be Z, the period (cycle) Z must have at least N×M slots.

Next, the following describes a specific example of a method ofallocating precoding matrices in order to achieve an arrangement ofsymbols with the method of allocating precoding matrices shown in FIGS.72A, 72B, 73A, and 73B.

First, the method of allocating precoding matrices in the frequencydomain is to allocate precoding matrices by incrementing the indexnumber one at a time, as described in Embodiment 17. When the indexnumber exceeds the number of prepared precoding matrices, allocationreturns to precoding matrix #1 and continues.

When allocating precoded symbols in the time domain as well, precodingmatrices are allocated by adding Sc, as described in Embodiment 17, yetthe conditions for Sc differ from those described in Embodiment 17.

The conditions for Sc described in Embodiment 17 are, in the presentembodiment, that when the differing range is expanded to N×M datasymbols, i.e. M symbols in the time domain and N symbols in thefrequency domain, then letting L be the larger of the values N and M, Scis equal to or greater than L symbols and equal to or less than Z−Lsymbols. (Let the hopping period (cycle) in the method of regularlyhopping between precoding matrices have Z slots.) However, when N M, theabove condition need not be satisfied in some cases.

Note that when Sc is set to a larger number than L, a larger number ofdifferent precoding matrices than N×M is necessary for the value of Z.In other words, it is preferable to set the hopping period (cycle) to belarge.

In the case of the 3×3 differing range in FIGS. 72A, 72B, 73A, and 73B,since L is 3, it is necessary for Sc to be an integer equal to orgreater than 3 and equal to or less than Z−3.

In other words, when the precoding matrix used for the symbol in carrierf₁ at time t1 is precoding matrix #1 and the differing range is 3×3, theprecoding matrix used for the symbol in carrier f1 at time t2 is 1+3,i.e. precoding matrix #4.

FIGS. 74A and 74B show the arrangement of symbols in a modulated signalwhen implementing precoding after allocating precoding matrices with thediffering range shown in FIGS. 72A and 72B. As is clear from FIGS. 74Aand 74B, different precoding matrices are used for the symbols in thediffering range at any location.

With reference to FIGS. 74A and 74B, the following structure has beendescribed. Precoding matrices are allocated in the frequency domain byincrementing the index number of the precoding matrices one at a time.When the index number exceeds the number of prepared precoding matrices,allocation returns to precoding matrix #1 and continues. When allocatingprecoded symbols in the time domain, precoding matrices are allocated byadding Sc, as also described in Embodiment 17. However, as in Embodiment17, the present invention may be similarly implemented by thinking ofthe vertical axis as frequency and the horizontal axis as time in FIGS.74A and 74B. Precoding matrices are then allocated in the time domain byincrementing the index number of the precoding matrices one at a time.When the index number exceeds the number of prepared precoding matrices,allocation returns to precoding matrix #1 and continues. When allocatingprecoded symbols in the frequency domain, precoding matrices areallocated by adding Sc, as also described in Embodiment 17. In this caseas well, the above conditions of Sc are important.

FIGS. 75A and 75B show examples of frame structure with a differingrange of 3×5, and FIGS. 76A and 76B show the arrangement of symbols in amodulated signal that are precoded with these frame structures.

As is clear from FIGS. 76A and 76B, the precoding matrices allocated inthe time domain are shifted by three symbols in the frequency domain inthe differing range. Furthermore, in FIGS. 76A and 76B, precodingmatrices that are all different from each other are allocated to thesymbols in the differing range at any location.

From the examples in FIGS. 76A and 76B, the conditions on Sc describedin Embodiment 17 can be thought of as follows when the differing rangeis expanded to N×M data symbols, i.e. M symbols in the time domain and Nsymbols in the frequency domain, and when N≠M.

Let the index number of precoding matrices in the frequency domain beincremented one at a time. When the index number exceeds the number ofprepared precoding matrices, allocation returns to precoding matrix #1and continues. When allocating precoded symbols in the time domain,precoding matrices are allocated by adding Sc, as described inEmbodiment 17. In this case, Sc must be equal to or greater than Nsymbols and equal to or less than Z−N. (Let the hopping period (cycle)in the method of regularly hopping between precoding matrices have Zslots.)

However, even when Sc is set according to the above conditions, in somecases the precoding matrices allocated to the symbols in the differingrange may not all be different. To achieve a structure in which all ofthe precoding matrices allocated to the symbols in the differing rangeare different, the size of the hopping period (cycle) should be set to alarge number.

Let the index number of precoding matrices in the time domain beincremented one at a time. When the index number exceeds the number ofprepared precoding matrices, allocation returns to precoding matrix #1and continues. When allocating precoded symbols in the frequency domain,precoding matrices are allocated by adding Sc, as described inEmbodiment 17. In this case, Sc must be equal to or greater than Msymbols and equal to or less than Z−M.

However, even when Sc is set according to the above conditions, in somecases the precoding matrices allocated to the symbols in the differingrange may not all be different. To achieve a structure in which all ofthe precoding matrices allocated to the symbols in the differing rangeare different, the size of the hopping period (cycle) should beincreased.

It is obvious that FIGS. 76A and 76B satisfy the above conditions. Withreference to FIGS. 76A and 76B, the following case has been described.Precoding matrices are allocated in the frequency domain by incrementingthe index number of the precoding matrices one at a time. When the indexnumber exceeds the number of prepared precoding matrices, allocationreturns to precoding matrix #1 and continues. When allocating precodedsymbols in the time domain, precoding matrices are allocated by addingSc, as also described in Embodiment 17. However, as in Embodiment 17,the present invention may be similarly implemented by thinking of thevertical axis as frequency and the horizontal axis as time in FIGS. 76Aand 76B. Precoding matrices are then allocated in the time domain byincrementing the index number of the precoding matrices one at a time.When the index number exceeds the number of prepared precoding matrices,allocation returns to precoding matrix #1 and continues. When allocatingprecoded symbols in the frequency domain, precoding matrices areallocated by adding Sc, as also described in Embodiment 17. In this caseas well, the above conditions of Sc are important.

Furthermore, while a structure has been described in which precodingmatrices are shifted by Sc in the time domain and are shifted one at atime in the frequency domain, precoding matrices may be allocated byshifting precoding matrices one at a time in the time domain and by Scin the frequency domain, as described in Embodiment 17 with reference toFIGS. 65A, 65B, 66A, and 66B.

Additionally, the precoding matrices used for all of the symbols in anydiffering range may differ from each other in a diamond-like differingrange as well, as shown in FIGS. 77A and 77B.

In this case, however, in order to satisfy the above conditions, thenecessary number of precoding matrices is the maximum number of symbolsin the frequency domain multiplied by the maximum number of symbols inthe time domain in the diamond-like differing range. In other words, inthe diamond-like differing range shown in FIGS. 77A and 77B, in order toachieve an arrangement in which all of the precoding matrices used forall of the symbols differ from each other, 25 precoding matrices arenecessary (5×5, i.e. the maximum number of symbols in the differingrange in the frequency domain multiplied by the maximum number ofsymbols in the differing range in the time domain). Adopting such adiamond-like differing range is substantially equivalent to a symbolarrangement with a differing range yielded by the smallest rectanglethat encloses the diamond-like differing range.

FIGS. 78A and 78B show actual symbol arrangements when allocatingprecoding matrices using the diamond-like differing range shown in FIGS.77A and 77B. In FIGS. 78A and 78B, it is clear that all of the precodingmatrices allocated to the symbols included in any diamond-like differingrange differ from each other.

In this way, even when the range in which all of the precoding matricesallocated to symbols differ from each other is expanded from fivesymbols as shown in Embodiment 17, a method can be implemented toallocate precoding matrices while incrementing by one, and shifting bySc, the index of the precoding matrices in the frequency and the timedomains.

While conditions have been described when allocating only data symbols,as in Embodiment 17, the following describes the arrangement of datasymbols when pilot symbols are inserted, as described in Embodiment 18.

One example of symbol arrangement when pilot symbols are inserted sharesthe concept described in Embodiment 18. Namely, since the locations atwhich pilot symbols are inserted are predetermined, at each locationwhere a pilot symbol is inserted, the number of the precoding matrixthat would be allocated if a pilot symbol were not inserted is skippedbefore multiplying the precoding matrix with the next symbol. In otherwords, at locations where pilot symbols are inserted, the number of theprecoding matrix allocated to the next symbol is increased more.Specifically, when incrementing the index one at a time, the index ofthe precoding matrix is incremented by two over the precoding matrixallocated to the previous symbol, and when shifting by Sc, the index ofthe precoding matrix is increased by 2×Sc.

FIGS. 79A and 79B show examples of insertion of pilot symbols into thesymbol arrangements shown in FIGS. 74A and 74B. As shown in FIGS. 79Aand 79B, a method of allocating precoding matrices is implementedwhereby, at positions where pilot symbols are inserted, the number ofthe precoding matrix that would have been allocated if a data symbolwere present is skipped.

With this structure, a differing range that expands the range over whichdifferent precoding matrices are allocated is also compatible withinsertion of pilot symbols.

Information indicating the allocation method of precoding matrices shownin Embodiment 17 may be generated by the weighting informationgenerating unit 314 shown in Embodiment 1, and in accordance with thegenerated information, the weighting units 308A and 308B or the like mayperform precoding and transmit information corresponding to the aboveinformation to the communication partner. (This information need not betransmitted when a rule is predetermined, i.e. when the method ofallocating precoding matrices is determined in advance at thetransmission side and the reception side.) The communication partnerlearns of the allocation method of precoding matrices used by thetransmission device and, based on this knowledge, decodes precodedsymbols.

In the present embodiment, the case of transmitting modulated signalss1, s2 and modulated signals z1, z2 has been described, i.e. an exampleof two streams and two transmission signals. The number of streams andof transmission signals is not limited in this way, however, and maysimilarly be implemented by allocating precoding matrices when thenumber is larger than two. In other words, if streams of modulatedsignals s3, s4, . . . exist, and transmission signals z3, z4, . . .exist, then in z3 and z4, the index of the precoding matrices for thesymbols in frames in the frequency-time domains may be allocatedsimilarly to the modulated signals z1 and z2.

Embodiment 20

Embodiment 18 describes the case of incrementing the index of theprecoding matrix that is used, i.e. of not incrementing the index of theprecoding matrix for symbols other than data symbols. In the presentembodiment, FIGS. 80A, 80B, 81A, and 81B show the allocation ofprecoding matrices in a frame differing from the description of FIGS.70A and 70B in Embodiment 18. Note that, similar to Embodiment 18, FIGS.80A, 80B, 81A, and 81B show the frame structure in the time-frequencydomains for modulated signals z1, z2, as well as pilot symbols, datasymbols, and the index numbers of precoding matrices used for the datasymbols. “P” indicates a pilot symbol, whereas other squares are datasymbols. The #X for each data symbol indicates the index number of theprecoding matrix that is used.

As compared to FIGS. 70A and 70B, FIGS. 80A and 80B show an example of aperiod (cycle) with a larger size and a larger value of Sc in the methodof regularly hopping between precoding matrices. Furthermore, conditions<a>, <a′>, <b>, and <b′> described in Embodiment 18 are satisfied. Withthese conditions, the number of times that the precoding matrices arenot incremented does not change over time. Therefore, not incrementingthe precoding matrices has a reduced effect on the relationship betweenindex numbers of the data symbols. Accordingly, all of the data symbolsthat have data symbols adjacent thereto satisfy Condition #53.

As another example, FIGS. 81A and 81B show a case not satisfyingconditions <a>, <a′>, <b>, and <b′>. As is clear from 8100, for example,in FIGS. 81A and 81B, condition #53 is not satisfied. This is a resultof the great impact caused by not satisfying the conditions described inEmbodiment 18.

Embodiment B1

The following describes a structural example of an application of thetransmission methods and reception methods shown in the aboveembodiments and a system using the application.

FIG. 82 shows an example of the structure of a system that includesdevices implanting the transmission methods and reception methodsdescribed in the above embodiments. The transmission method andreception method described in the above embodiments are implemented in adigital broadcasting system 8200, as shown in FIG. 82, that includes abroadcasting station 8201 and a variety of reception devices such as atelevision 8211, a DVD recorder 8212, a Set Top Box (STB) 8213, acomputer 8220, an in-car television 8241, and a mobile phone 8230.Specifically, the broadcasting station 8201 transmits multiplexed data,in which video data, audio data, and the like are multiplexed, using thetransmission methods in the above embodiments over a predeterminedbroadcasting band.

An antenna (for example, antennas 8210 and 8240) internal to eachreception device, or provided externally and connected to the receptiondevice, receives the signal transmitted from the broadcasting station8201. Each reception device obtains the multiplexed data by using thereception methods in the above embodiments to demodulate the signalreceived by the antenna. In this way, the digital broadcasting system8200 obtains the advantageous effects of the present invention describedin the above embodiments.

The video data included in the multiplexed data has been coded with amoving picture coding method compliant with a standard such as MovingPicture Experts Group (MPEG)2, MPEG4-Advanced Video Coding (AVC), VC-1,or the like. The audio data included in the multiplexed data has beenencoded with an audio coding method compliant with a standard such asDolby Audio Coding (AC)-3, Dolby Digital Plus, Meridian Lossless Packing(MLP), Digital Theater Systems (DTS), DTS-HD, Pulse Coding Modulation(PCM), or the like.

FIG. 83 is a schematic view illustrating an exemplary structure of areception device 7900 for carrying out the reception methods describedin the above embodiments. The reception device 8300 shown in FIG. 83corresponds to a component that is included, for example, in thetelevision 8211, the DVD recorder 8212, the STB 8213, the computer 8220,the in-car television 8241, the mobile phone 8230, or the likeillustrated in FIG. 82. The reception device 8300 includes a tuner 8301,for transforming a high-frequency signal received by an antenna 8360into a baseband signal, and a demodulation unit 8302, for demodulatingmultiplexed data from the baseband signal obtained by frequencyconversion. The reception methods described in the above embodiments areimplemented in the demodulation unit 8302, thus obtaining theadvantageous effects of the present invention described in the aboveembodiments.

The reception device 8300 includes a stream input/output unit 8303, asignal processing unit 8304, an audio output unit 8306, and a videodisplay unit 8307. The stream input/output unit 8303 demultiplexes videoand audio data from multiplexed data obtained by the demodulation unit8302. The signal processing unit 8304 decodes the demultiplexed videodata into a video signal using an appropriate moving picture decodingmethod and decodes the demultiplexed audio data into an audio signalusing an appropriate audio decoding method. The audio output unit 8306,such as a speaker, produces audio output according to the decoded audiosignal. The video display unit 8307, such as a display monitor, producesvideo output according to the decoded video signal.

For example, the user may operate the remote control 8350 to select achannel (of a TV program or audio broadcast), so that informationindicative of the selected channel is transmitted to an operation inputunit 8310. In response, the reception device 8300 demodulates, fromamong signals received with the antenna 8360, a signal carried on theselected channel and applies error correction decoding, so thatreception data is extracted. At this time, the receiving device 8300receives control symbols included in a signal corresponding to theselected channel and containing information indicating the transmissionmethod (the transmission method, modulation method, error correctionmethod, and the like in the above embodiments) of the signal (exactly asshown in FIGS. 5 and 41). With this information, the reception device8300 is enabled to make appropriate settings for the receivingoperations, demodulation method, method of error correction decoding,and the like to duly receive data included in data symbols transmittedfrom a broadcasting station (base station). Although the abovedescription is directed to an example in which the user selects achannel using the remote control 8350, the same description applies toan example in which the user selects a channel using a selection keyprovided on the reception device 8300.

With the above structure, the user can view a broadcast program that thereception device 8300 receives by the reception methods described in theabove embodiments.

The reception device 8300 according to this embodiment may additionallyinclude a recording unit (drive) 8308 for recording various data onto arecording medium, such as a magnetic disk, optical disc, or anon-volatile semiconductor memory. Examples of data to be recorded bythe recording unit 8308 include data contained in multiplexed data thatis obtained as a result of demodulation and error correction by thedemodulation unit 8302, data equivalent to such data (for example, dataobtained by compressing the data), and data obtained by processing themoving pictures and/or audio. (Note here that there may be a case whereno error correction decoding is applied to a signal obtained as a resultof demodulation by the demodulation unit 8302 and where the receptiondevice 8300 conducts further signal processing after error correctiondecoding. The same holds in the following description where similarwording appears.) Note that the term “optical disc” used herein refersto a recording medium, such as Digital Versatile Disc (DVD) or BD(Blu-ray Disc), that is readable and writable with the use of a laserbeam. Further, the term “magnetic disk” used herein refers to arecording medium, such as a floppy disk (FD, registered trademark) orhard disk, that is writable by magnetizing a magnetic substance withmagnetic flux. Still further, the term “non-volatile semiconductormemory” refers to a recording medium, such as flash memory orferroelectric random access memory, composed of semiconductorelement(s). Specific examples of non-volatile semiconductor memoryinclude an SD card using flash memory and a flash Solid State Drive(SSD). It should be naturally appreciated that the specific types ofrecording media mentioned herein are merely examples, and any othertypes of recording mediums may be usable.

With the above structure, the user can record a broadcast program thatthe reception device 8300 receives with any of the reception methodsdescribed in the above embodiments, and time-shift viewing of therecorded broadcast program is possible anytime after the broadcast.

In the above description of the reception device 8300, the recordingunit 8308 records multiplexed data obtained as a result of demodulationand error correction by the demodulation unit 8302. However, therecording unit 8308 may record part of data extracted from the datacontained in the multiplexed data. For example, the multiplexed dataobtained as a result of demodulation and error correction by thedemodulation unit 8302 may contain contents of data broadcast service,in addition to video data and audio data. In this case, new multiplexeddata may be generated by multiplexing the video data and audio data,without the contents of broadcast service, extracted from themultiplexed data demodulated by the demodulation unit 8302, and therecording unit 8308 may record the newly generated multiplexed data.Alternatively, new multiplexed data may be generated by multiplexingeither of the video data and audio data contained in the multiplexeddata obtained as a result of demodulation and error correction decodingby the demodulation unit 8302, and the recording unit 8308 may recordthe newly generated multiplexed data. The recording unit 8308 may alsorecord the contents of data broadcast service included, as describedabove, in the multiplexed data.

The reception device 8300 described in this embodiment may be includedin a television, a recorder (such as DVD recorder, Blu-ray recorder, HDDrecorder, SD card recorder, or the like), or a mobile telephone. In sucha case, the multiplexed data obtained as a result of demodulation anderror correction decoding by the demodulation unit 8302 may contain datafor correcting errors (bugs) in software used to operate the televisionor recorder or in software used to prevent disclosure of personal orconfidential information. If such data is contained, the data isinstalled on the television or recorder to correct the software errors.Further, if data for correcting errors (bugs) in software installed inthe reception device 8300 is contained, such data is used to correcterrors that the reception device 8300 may have. This arrangement ensuresmore stable operation of the TV, recorder, or mobile phone in which thereception device 8300 is implemented.

Note that it may be the stream input/output unit 8303 that handlesextraction of data from the whole data contained in multiplexed dataobtained as a result of demodulation and error correction decoding bythe demodulation unit 8302 and multiplexing of the extracted data. Morespecifically, under instructions given from a control unit notillustrated in the figures, such as a CPU, the stream input/output unit8303 demultiplexes video data, audio data, contents of data broadcastservice etc. from the multiplexed data demodulated by the demodulationunit 8302, extracts specific pieces of data from the demultiplexed data,and multiplexes the extracted data pieces to generate new multiplexeddata. The data pieces to be extracted from demultiplexed data may bedetermined by the user or determined in advance for the respective typesof recording mediums.

With the above structure, the reception device 8300 is enabled toextract and record only data necessary to view a recorded broadcastprogram, which is effective to reduce the size of data to be recorded.

In the above description, the recording unit 8308 records multiplexeddata obtained as a result of demodulation and error correction decodingby the demodulation unit 8302. Alternatively, however, the recordingunit 8308 may record new multiplexed data generated by multiplexingvideo data newly yielded by encoding the original video data containedin the multiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8302. Here, the movingpicture coding method to be employed may be different from that used toencode the original video data, so that the data size or bit rate of thenew video data is smaller than the original video data. Here, the movingpicture coding method used to generate new video data may be of adifferent standard from that used to generate the original video data.Alternatively, the same moving picture coding method may be used butwith different parameters. Similarly, the recording unit 8308 may recordnew multiplexed data generated by multiplexing audio data newly obtainedby encoding the original audio data contained in the multiplexed dataobtained as a result of demodulation and error correction decoding bythe demodulation unit 8302. Here, the audio coding method to be employedmay be different from that used to encode the original audio data, suchthat the data size or bit rate of the new audio data is smaller than theoriginal audio data.

The process of converting the original video or audio data contained inthe multiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8302 into the video oraudio data of a different data size or bit rate is performed, forexample, by the stream input/output unit 8303 and the signal processingunit 8304. More specifically, under instructions given from the controlunit such as the CPU, the stream input/output unit 8303 demultiplexesvideo data, audio data, contents of data broadcast service etc. from themultiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8302. Under instructionsgiven from the control unit, the signal processing unit 8304 convertsthe demultiplexed video data and audio data respectively using a motionpicture coding method and an audio coding method each different from themethod that was used in the conversion applied to obtain the video andaudio data. Under instructions given from the control unit, the streaminput/output unit 8303 multiplexes the newly converted video data andaudio data to generate new multiplexed data. Note that the signalprocessing unit 8304 may conduct the conversion of either or both of thevideo or audio data according to instructions given from the controlunit. In addition, the sizes of video data and audio data to be obtainedby encoding may be specified by a user or determined in advance for thetypes of recording mediums.

With the above arrangement, the reception device 8300 is enabled torecord video and audio data after converting the data to a sizerecordable on the recording medium or to a size or bit rate that matchesthe read or write rate of the recording unit 8308. This arrangementenables the recoding unit to duly record a program, even if the sizerecordable on the recording medium is smaller than the data size of themultiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8302, or if the rate atwhich the recording unit records or reads is lower than the bit rate ofthe multiplexed data. Consequently, time-shift viewing of the recordedprogram by the user is possible anytime after the broadcast.

Furthermore, the reception device 8300 additionally includes a streamoutput interface (IF) 8309 for transmitting multiplexed data demodulatedby the demodulation unit 8302 to an external device via a transportmedium 8330. In one example, the stream output IF 8309 may be a radiocommunication device that transmits multiplexed data via a wirelessmedium (equivalent to the transport medium 8330) to an external deviceby modulating the multiplexed data with in accordance with a wirelesscommunication method compliant with a wireless communication standardsuch as Wi-Fi (registered trademark, a set of standards including IEEE802.11a, IEEE 802.11b, IEEE 802.11g, and IEEE 802.11n), WiGiG, WirelessHD, Bluetooth, ZigBee, or the like. The stream output IF 8309 may alsobe a wired communication device that transmits multiplexed data via atransmission line (equivalent to the transport medium 8330) physicallyconnected to the stream output IF 8309 to an external device, modulatingthe multiplexed data using a communication method compliant with wiredcommunication standards, such as Ethernet (registered trademark),Universal Serial Bus (USB), Power Line Communication (PLC), orHigh-Definition Multimedia Interface (HDMI).

With the above structure, the user can use, on an external device,multiplexed data received by the reception device 8300 using thereception method described according to the above embodiments. The usageof multiplexed data by the user mentioned herein includes use of themultiplexed data for real-time viewing on an external device, recordingof the multiplexed data by a recording unit included in an externaldevice, and transmission of the multiplexed data from an external deviceto a yet another external device.

In the above description of the reception device 8300, the stream outputIF 8309 outputs multiplexed data obtained as a result of demodulationand error correction decoding by the demodulation unit 8302. However,the reception device 8300 may output data extracted from data containedin the multiplexed data, rather than the whole data contained in themultiplexed data. For example, the multiplexed data obtained as a resultof demodulation and error correction decoding by the demodulation unit8302 may contain contents of data broadcast service, in addition tovideo data and audio data. In this case, the stream output IF 8309 mayoutput multiplexed data newly generated by multiplexing video and audiodata extracted from the multiplexed data obtained as a result ofdemodulation and error correction decoding by the demodulation unit8302. In another example, the stream output IF 8309 may outputmultiplexed data newly generated by multiplexing either of the videodata and audio data contained in the multiplexed data obtained as aresult of demodulation and error correction decoding by the demodulationunit 8302.

Note that it may be the stream input/output unit 8303 that handlesextraction of data from the whole data contained in multiplexed dataobtained as a result of demodulation and error correction decoding bythe demodulation unit 8302 and multiplexing of the extracted data. Morespecifically, under instructions given from a control unit notillustrated in the figures, such as a Central Processing Unit (CPU), thestream input/output unit 8303 demultiplexes video data, audio data,contents of data broadcast service etc. from the multiplexed datademodulated by the demodulation unit 8302, extracts specific pieces ofdata from the demultiplexed data, and multiplexes the extracted datapieces to generate new multiplexed data. The data pieces to be extractedfrom demultiplexed data may be determined by the user or determined inadvance for the respective types of the stream output IF 8309.

With the above structure, the reception device 8300 is enabled toextract and output only data necessary for an external device, which iseffective to reduce the bandwidth used to output the multiplexed data.

In the above description, the stream output IF 8309 outputs multiplexeddata obtained as a result of demodulation and error correction decodingby the demodulation unit 8302. Alternatively, however, the stream outputIF 8309 may output new multiplexed data generated by multiplexing videodata newly yielded by encoding the original video data contained in themultiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8302. The new video data isencoded with a moving picture coding method different from that used toencode the original video data, so that the data size or bit rate of thenew video data is smaller than the original video data. Here, the movingpicture coding method used to generate new video data may be of adifferent standard from that used to generate the original video data.Alternatively, the same moving picture coding method may be used butwith different parameters. Similarly, the stream output IF 8309 mayoutput new multiplexed data generated by multiplexing audio data newlyobtained by encoding the original audio data contained in themultiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8302. The new audio data isencoded with an audio coding method different from that used to encodethe original audio data, such that the data size or bit rate of the newaudio data is smaller than the original audio data.

The process of converting the original video or audio data contained inthe multiplexed data obtained as a result of demodulation and errorcorrection decoding by the demodulation unit 8302 into the video oraudio data of a different data size of bit rate is performed, forexample, by the stream input/output unit 8303 and the signal processingunit 8304. More specifically, under instructions given from the controlunit, the stream input/output unit 8303 demultiplexes video data, audiodata, contents of data broadcast service etc. from the multiplexed dataobtained as a result of demodulation and error correction decoding bythe demodulation unit 8302. Under instructions given from the controlunit, the signal processing unit 8304 converts the demultiplexed videodata and audio data respectively using a motion picture coding methodand an audio coding method each different from the method that was usedin the conversion applied to obtain the video and audio data. Underinstructions given from the control unit, the stream input/output unit8303 multiplexes the newly converted video data and audio data togenerate new multiplexed data. Note that the signal processing unit 8304may perform the conversion of either or both of the video or audio dataaccording to instructions given from the control unit. In addition, thesizes of video data and audio data to be obtained by conversion may bespecified by the user or determined in advance for the types of thestream output IF 8309.

With the above structure, the reception device 8300 is enabled to outputvideo and audio data after converting the data to a bit rate thatmatches the transfer rate between the reception device 8300 and anexternal device. This arrangement ensures that even if multiplexed dataobtained as a result of demodulation and error correction decoding bythe demodulation unit 8302 is higher in bit rate than the data transferrate to an external device, the stream output IF duly outputs newmultiplexed data at an appropriate bit rate to the external device.Consequently, the user can use the new multiplexed data on anothercommunication device.

Furthermore, the reception device 8300 also includes an audio and visualoutput interface (hereinafter, AV output IF) 8311 that outputs video andaudio signals decoded by the signal processing unit 8304 to an externaldevice via an external transport medium. In one example, the AV outputIF 8311 may be a wireless communication device that transmits modulatedvideo and audio signals via a wireless medium to an external device,using a wireless communication method compliant with wirelesscommunication standards, such as Wi-Fi (registered trademark), which isa set of standards including IEEE 802.11a, IEEE 802.11b, IEEE 802.11g,and IEEE 802.11n, WiGiG, Wireless HD, Bluetooth, ZigBee, or the like. Inanother example, the stream output IF 8309 may be a wired communicationdevice that transmits modulated video and audio signals via atransmission line physically connected to the stream output IF 8309 toan external device, using a communication method compliant with wiredcommunication standards, such as Ethernet (registered trademark), USB,PLC, HDMI, or the like. In yet another example, the stream output IF8309 may be a terminal for connecting a cable to output the video andaudio signals in analog form.

With the above structure, the user is allowed to use, on an externaldevice, the video and audio signals decoded by the signal processingunit 8304.

Furthermore, the reception device 8300 additionally includes anoperation input unit 8310 for receiving a user operation. According tocontrol signals indicative of user operations input to the operationinput unit 8310, the reception device 8300 performs various operations,such as switching the power ON or OFF, switching the reception channel,switching the display of subtitle text ON or OFF, switching the displayof subtitle text to another language, changing the volume of audiooutput of the audio output unit 8306, and changing the settings ofchannels that can be received.

Additionally, the reception device 8300 may have a function ofdisplaying the antenna level indicating the quality of the signal beingreceived by the reception device 8300. Note that the antenna level is anindicator of the reception quality calculated based on, for example, theReceived Signal Strength Indication, Received Signal Strength Indicator(RSSI), received field strength, Carrier-to-noise power ratio (C/N), BitError Rate (BER), packet error rate, frame error rate, and channel stateinformation of the signal received on the reception device 8300. Inother words, the antenna level is a signal indicating the level andquality of the received signal. In this case, the demodulation unit 8302also includes a reception quality measuring unit for measuring thereceived signal characteristics, such as RSSI, received field strength,C/N, BER, packet error rate, frame error rate, and channel stateinformation. In response to a user operation, the reception device 8300displays the antenna level (i.e., signal indicating the level andquality of the received signal) on the video display unit 8307 in amanner identifiable by the user. The antenna level (i.e., signalindicating the level and quality of the received signal) may benumerically displayed using a number that represents RSSI, receivedfield strength, C/N, BER, packet error rate, frame error rate, channelstate information or the like. Alternatively, the antenna level may bedisplayed using an image representing RSSI, received field strength,C/N, BER, packet error rate, frame error rate, channel state informationor the like. Furthermore, the reception device 8300 may display aplurality of antenna levels (signals indicating the level and quality ofthe received signal) calculated for each of the plurality of streams s1,s2, . . . received and separated using the reception methods shown inthe above embodiments, or one antenna level (signal indicating the leveland quality of the received signal) calculated from the plurality ofstreams s1, s2, . . . . When video data and audio data composing aprogram are transmitted hierarchically, the reception device 8300 mayalso display the signal level (signal indicating the level and qualityof the received signal) for each hierarchical level.

With the above structure, users are able to grasp the antenna level(signal indicating the level and quality of the received signal)numerically or visually during reception with the reception methodsshown in the above embodiments.

Although the reception device 8300 is described above as having theaudio output unit 8306, video display unit 8307, recording unit 8308,stream output IF 8309, and AV output IF 8311, it is not necessary forthe reception device 8300 to have all of these units. As long as thereception device 8300 is provided with at least one of the unitsdescribed above, the user is enabled to use multiplexed data obtained asa result of demodulation and error correction decoding by thedemodulation unit 8302. The reception device 8300 may therefore includeany combination of the above-described units depending on its intendeduse.

Multiplexed Data

The following is a detailed description of an exemplary structure ofmultiplexed data. The data structure typically used in broadcasting isan MPEG2 transport stream (TS), so therefore the following descriptionis given by way of an example related to MPEG2-TS. It should benaturally appreciated, however, that the data structure of multiplexeddata transmitted by the transmission and reception methods described inthe above embodiments is not limited to MPEG2-TS and the advantageouseffects of the above embodiments are achieved even if any other datastructure is employed.

FIG. 84 is a view illustrating an exemplary multiplexed data structure.As illustrated in FIG. 84, multiplexed data is obtained by multiplexingone or more elementary streams, which are elements constituting abroadcast program (program or an event which is part of a program)currently provided through respective services. Examples of elementarystreams include a video stream, audio stream, presentation graphics (PG)stream, and interactive graphics (IG) stream. In the case where abroadcast program carried by multiplexed data is a movie, the videostreams represent main video and sub video of the movie, the audiostreams represent main audio of the movie and sub audio to be mixed withthe main audio, and the PG stream represents subtitles of the movie. Theterm “main video” used herein refers to video images normally presentedon a screen, whereas “sub video” refers to video images (for example,images of text explaining the outline of the movie) to be presented in asmall window inserted within the video images. The IG stream representsan interactive display constituted by presenting GUI components on ascreen.

Each stream contained in multiplexed data is identified by an identifiercalled PID uniquely assigned to the stream. For example, the videostream carrying main video images of a movie is assigned with “0x1011”,each audio stream is assigned with a different one of “0x1100” to“0x111F”, each PG stream is assigned with a different one of “0x1200” to“0x121F”, each IG stream is assigned with a different one of “0x1400” to“0x141F”, each video stream carrying sub video images of the movie isassigned with a different one of “0x1B00” to “0x1B1F”, each audio streamof sub-audio to be mixed with the main audio is assigned with adifferent one of “0x1A00” to “0x1A1F”.

FIG. 85 is a schematic view illustrating an example of how therespective streams are multiplexed into multiplexed data. First, a videostream 8501 composed of a plurality of video frames is converted into aPES packet sequence 8502 and then into a TS packet sequence 8503,whereas an audio stream 8504 composed of a plurality of audio frames isconverted into a PES packet sequence 8505 and then into a TS packetsequence 8506. Similarly, the PG stream 8511 is first converted into aPES packet sequence 8512 and then into a TS packet sequence 8513,whereas the IG stream 8514 is converted into a PES packet sequence 8515and then into a TS packet sequence 8516. The multiplexed data 8517 isobtained by multiplexing the TS packet sequences (8503, 8506, 8513 and8516) into one stream.

FIG. 86 illustrates the details of how a video stream is divided into asequence of PES packets. In FIG. 86, the first tier shows a sequence ofvideo frames included in a video stream. The second tier shows asequence of PES packets. As indicated by arrows yy1, yy2, yy3, and yy4shown in FIG. 86, a plurality of video presentation units, namely Ipictures, B pictures, and P pictures, of a video stream are separatelystored into the payloads of PES packets on a picture-by-picture basis.Each PES packet has a PES header and the PES header stores aPresentation Time-Stamp (PTS) and Decoding Time-Stamp (DTS) indicatingthe display time and decoding time of a corresponding picture.

FIG. 87 illustrates the format of a TS packet to be eventually writtenas multiplexed data. The TS packet is a fixed length packet of 188 bytesand has a 4-byte TS header containing such information as PIDidentifying the stream and a 184-byte TS payload carrying actual data.The PES packets described above are divided to be stored into the TSpayloads of TS packets. In the case of BD-ROM, each TS packet isattached with a TP_Extra Header of 4 bytes to build a 192-byte sourcepacket, which is to be written as multiplexed data. The TP_Extra Headercontains such information as an Arrival Time Stamp (ATS). The ATSindicates a time for starring transfer of the TS packet to the PIDfilter of a decoder. As shown on the lowest tier in FIG. 87, multiplexeddata includes a sequence of source packets each bearing a source packetnumber (SPN), which is a number incrementing sequentially from the startof the multiplexed data.

In addition to the TS packets storing streams such as video, audio, andPG streams, multiplexed data also includes TS packets storing a ProgramAssociation Table (PAT), a Program Map Table (PMT), and a Program ClockReference (PCR). The PAT in multiplexed data indicates the PID of a PMTused in the multiplexed data, and the PID of the PAT is “0”. The PMTincludes PIDs identifying the respective streams, such as video, audioand subtitles, contained in multiplexed data and attribute information(frame rate, aspect ratio, and the like) of the streams identified bythe respective PIDs. In addition, the PMT includes various types ofdescriptors relating to the multiplexed data. One of such descriptorsmay be copy control information indicating whether or not copying of themultiplexed data is permitted. The PCR includes information forsynchronizing the Arrival Time Clock (ATC), which is the time axis ofATS, with the System Time Clock (STC), which is the time axis of PTS andDTS. More specifically, the PCR packet includes information indicatingan STC time corresponding to the ATS at which the PCR packet is to betransferred.

FIG. 88 is a view illustrating the data structure of the PMT in detail.The PMT starts with a PMT header indicating the length of data containedin the PMT. Following the PMT header, descriptors relating to themultiplexed data are disposed. One example of a descriptor included inthe PMT is copy control information described above. Following thedescriptors, pieces of stream information relating to the respectivestreams included in the multiplexed data are arranged. Each piece ofstream information is composed of stream descriptors indicating a streamtype identifying a compression codec employed for a correspondingstream, a PID of the stream, and attribute information (frame rate,aspect ratio, and the like) of the stream. The PMT includes as manystream descriptors as the number of streams included in the multiplexeddata.

When recorded onto a recoding medium, for example, the multiplexed datais recorded along with a multiplexed data information file.

FIG. 89 is a view illustrating the structure of the multiplexed datainformation file. As illustrated in FIG. 89, the multiplexed datainformation file is management information of corresponding multiplexeddata and is composed of multiplexed data information, stream attributeinformation, and an entry map. Note that multiplexed data informationfiles and multiplexed data are in a one-to-one relationship.

As illustrated in FIG. 89, the multiplexed data information is composedof a system rate, playback start time, and playback end time. The systemrate indicates the maximum transfer rate of the multiplexed data to thePID filter of a system target decoder, which is described later. Themultiplexed data includes ATSs at intervals set so as not to exceed thesystem rate. The playback start time is set to the time specified by thePTS of the first video frame in the multiplexed data, whereas theplayback end time is set to the time calculated by adding the playbackperiod of one frame to the PTS of the last video frame in themultiplexed data.

FIG. 90 illustrates the structure of stream attribute informationcontained in multiplexed data information file. As illustrated in FIG.90, the stream attribute information includes pieces of attributeinformation of the respective streams included in multiplexed data, andeach piece of attribute information is registered with a correspondingPID. That is, different pieces of attribute information are provided fordifferent streams, namely a video stream, an audio stream, a PG streamand an IG stream. The video stream attribute information indicates thecompression codec employed to compress the video stream, the resolutionsof individual pictures constituting the video stream, the aspect ratio,the frame rate, and so on. The audio stream attribute informationindicates the compression codec employed to compress the audio stream,the number of channels included in the audio stream, the language of theaudio stream, the sampling frequency, and so on. These pieces ofinformation are used to initialize a decoder before playback by aplayer.

In the present embodiment, from among the pieces of information includedin the multiplexed data, the stream type included in the PMT is used. Inthe case where the multiplexed data is recorded on a recording medium,the video stream attribute information included in the multiplexed datainformation file is used. More specifically, the moving picture codingmethod and device described in any of the above embodiments may bemodified to additionally include a step or unit of setting a specificpiece of information in the stream type included in the PMT or in thevideo stream attribute information. The specific piece of information isfor indicating that the video data is generated by the moving picturecoding method and device described in the embodiment. With the abovestructure, video data generated by the moving picture coding method anddevice described in any of the above embodiments is distinguishable fromvideo data compliant with other standards.

FIG. 91 illustrates an exemplary structure of a video and audio outputdevice 9100 that includes a reception device 9104 for receiving amodulated signal carrying video and audio data or data for databroadcasting from a broadcasting station (base station). Note that thestructure of the reception device 9104 corresponds to the receptiondevice 8300 illustrated in FIG. 83. The video and audio output device9100 is installed with an Operating System (OS), for example, and alsowith a transmission device 9106 (a device for a wireless Local AreaNetwork (LAN) or Ethernet, for example) for establishing an Internetconnection. With this structure, hypertext (World Wide Web (WWW)) 9103provided over the Internet can be displayed on a display area 9101simultaneously with images 9102 reproduced on the display area 9101 fromthe video and audio data or data provided by data broadcasting. Byoperating a remote control (which may be a mobile phone or keyboard)9107, the user can make a selection on the images 9102 reproduced fromdata provided by data broadcasting or the hypertext 9103 provided overthe Internet to change the operation of the video and audio outputdevice 9100. For example, by operating the remote control to make aselection on the hypertext 9103 provided over the Internet, the user canchange the WWW site currently displayed to another site. Alternatively,by operating the remote control 9107 to make a selection on the images9102 reproduced from the video or audio data or data provided by thedata broadcasting, the user can transmit information indicating aselected channel (such as a selected broadcast program or audiobroadcasting). In response, an interface (IF) 9105 acquires informationtransmitted from the remote control, so that the reception device 9104operates to obtain reception data by demodulation and error correctionof a signal carried on the selected channel. At this time, the receptiondevice 9104 receives control symbols included in a signal correspondingto the selected channel and containing information indicating thetransmission method of the signal (exactly as shown in FIGS. 5 and 41).With this information, the reception device 9104 is enabled to makeappropriate settings for the receiving operations, demodulation method,method of error correction decoding, and the like to duly receive dataincluded in data symbols transmitted from a broadcasting station (basestation). Although the above description is directed to an example inwhich the user selects a channel using the remote control 9107, the samedescription applies to an example in which the user selects a channelusing a selection key provided on the video and audio output device9100.

In addition, the video and audio output device 9100 may be operated viathe Internet. For example, a terminal connected to the Internet may beused to make settings on the video and audio output device 9100 forpre-programmed recording (storing). (The video and audio output device9100 therefore would have the recording unit 8308 as illustrated in FIG.83.) In this case, before starting the pre-programmed recording, thevideo and audio output device 9100 selects the channel, so that thereceiving device 9104 operates to obtain reception data by demodulationand error correction decoding of a signal carried on the selectedchannel. At this time, the reception device 9104 receives controlsymbols included in a signal corresponding to the selected channel andcontaining information indicating the transmission method (thetransmission method, modulation method, error correction method, and thelike in the above embodiments) of the signal (exactly as shown in FIGS.5 and 41). With this information, the reception device 9104 is enabledto make appropriate settings for the receiving operations, demodulationmethod, method of error correction decoding, and the like to dulyreceive data included in data symbols transmitted from a broadcastingstation (base station).

Supplementary Explanation

In the present description, it is considered that acommunications/broadcasting device such as a broadcast station, a basestation, an access point, a terminal, a mobile phone, or the like isprovided with the transmission device, and that a communications devicesuch as a television, radio, terminal, personal computer, mobile phone,access point, base station, or the like is provided with the receptiondevice. Additionally, it is considered that the transmission device andthe reception device in the present description have a communicationsfunction and are capable of being connected via some sort of interface(such as a USB) to a device for executing applications for a television,radio, personal computer, mobile phone, or the like.

Furthermore, in the present embodiment, symbols other than data symbols,such as pilot symbols (preamble, unique word, postamble, referencesymbol, and the like), symbols for control information, and the like maybe arranged in the frame in any way. While the terms “pilot symbol” and“symbols for control information” have been used here, any term may beused, since the function itself is what is important.

It suffices for a pilot symbol, for example, to be a known symbolmodulated with PSK modulation in the transmission and reception devices(or for the reception device to be able to synchronize in order to knowthe symbol transmitted by the transmission device). The reception deviceuses this symbol for frequency synchronization, time synchronization,channel estimation (estimation of Channel State Information (CSI) foreach modulated signal), detection of signals, and the like.

A symbol for control information is for transmitting information otherthan data (of applications or the like) that needs to be transmitted tothe communication partner for achieving communication (for example, themodulation method, error correction coding method, coding ratio of theerror correction coding method, setting information in the upper layer,and the like).

Note that the present invention is not limited to the above embodimentsand may be embodied with a variety of modifications. For example, theabove embodiments describe communications devices, but the presentinvention is not limited to these devices and may be implemented assoftware for the corresponding communications method.

Furthermore, a precoding hopping method used in a method of transmittingtwo modulated signals from two antennas has been described, but thepresent invention is not limited in this way. The present invention maybe also embodied as a precoding hopping method for similarly changingprecoding weights (matrices) in the context of a method whereby fourmapped signals are precoded to generate four modulated signals that aretransmitted from four antennas, or more generally, whereby N mappedsignals are precoded to generate N modulated signals that aretransmitted from N antennas.

In the present description, the terms “precoding”, “precoding matrix”,“precoding weight matrix” and the like are used, but any term may beused (such as “codebook”, for example) since the signal processingitself is what is important in the present invention.

Furthermore, in the present description, the reception device has beendescribed as using ML calculation, APP, Max-log APP, ZF, MMSE, or thelike, which yields soft decision results (log-likelihood, log-likelihoodratio) or hard decision results (“0” or “1”) for each bit of datatransmitted by the transmission device. This process may be referred toas detection, demodulation, estimation, or separation.

Different data may be transmitted in streams s1(t) and s2(t), or thesame data may be transmitted.

Assume that precoded baseband signals z1(i), z2(i) (where i representsthe order in terms of time or frequency (carrier)) are generated byprecoding baseband signals s1(i) and s2(i) for two streams whileregularly hopping between precoding matrices. Let the in-phase componentI and the quadrature component Q of the precoded baseband signal z1(i)be I₁(i) and Q₁(i) respectively, and let the in-phase component I andthe quadrature component Q of the precoded baseband signal z2(i) beI₂(i) and Q₂(i) respectively. In this case, the baseband components maybe switched, and modulated signals corresponding to the switchedbaseband signal r1(i) and the switched baseband signal r2(i) may betransmitted from different antennas at the same time and over the samefrequency by transmitting a modulated signal corresponding to theswitched baseband signal r1(i) from transmit antenna 1 and a modulatedsignal corresponding to the switched baseband signal r2(i) from transmitantenna 2 at the same time and over the same frequency. Basebandcomponents may be switched as follows.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₁(i) and Q₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be I₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₁(i) and I₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be Q₁(i) and Q₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be Q₁(i) and Q₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₁(i) and I₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be Q₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be Q₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be I₁(i) and Q₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be Q₁(i) and I₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be Q₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be I₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r1(i) be Q₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr2(i) be Q₁(i) and I₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₁(i) and I₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be Q₁(i) and Q₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be Q₁(i) and Q₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₁(i) and I₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be Q₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be Q₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₁(i) and Q₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be I₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be I₁(i) and Q₂(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be Q₁(i) and I₂(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be Q₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be I₂(i) and Q₁(i) respectively.

Let the in-phase component and the quadrature component of the switchedbaseband signal r2(i) be Q₂(i) and I₁(i) respectively, and the in-phasecomponent and the quadrature component of the switched baseband signalr1(i) be Q₁(i) and I₂(i) respectively.

In the above description, signals in two streams are precoded, andin-phase components and quadrature components of the precoded signalsare switched, but the present invention is not limited in this way.Signals in more than two streams may be precoded, and the in-phasecomponents and quadrature components of the precoded signals may beswitched.

Each of the transmit antennas of the transmission device and the receiveantennas of the reception device shown in the figures may be formed by aplurality of antennas.

In this description, the symbol “∀” represents the universal quantifier,and the symbol “∃” represents the existential quantifier.

Furthermore, in this description, the units of phase, such as argument,in the complex plane are radians.

When using the complex plane, complex numbers may be shown in polar formby polar coordinates. If a complex number z=a+jb (where a and b are realnumbers and j is an imaginary unit) corresponds to a point (a, b) on thecomplex plane, and this point is represented in polar coordinates as [r,θ], then the following equations hold.a=r×cos θb=r×sin θr=√{square root over (a ² +b ²)}  Math 303

r is the absolute value of z (r=|z|), and θ is the argument.Furthermore, z=a+jb is represented as re^(jθ.)

In the description of the present invention, the baseband signal,modulated signal s1, modulated signal s2, modulated signal z1, andmodulated signal z2 are complex signals. Complex signals are representedas I+jQ (where j is an imaginary unit), I being the in-phase signal, andQ being the quadrature signal. In this case, I may be zero, or Q may bezero.

The method of allocating different precoding matrices to frames (in thetime domain and/or the frequency domain) described in this description(for example, Embodiment 1 and Embodiments 17 through 20) may beimplemented using other precoding matrices than the different precodingmatrices in this description. The method of regularly hopping betweenprecoding matrices may also coexist with or be switched with othertransmission methods. In this case as well, the method of regularlyhopping between different precoding matrices described in thisdescription may be implemented using different precoding matrices.

FIG. 59 shows an example of a broadcasting system that uses the methodof regularly hopping between precoding matrices described in thisdescription. In FIG. 59, a video encoder 5901 receives video images asinput, encodes the video images, and outputs encoded video images asdata 5902. An audio encoder 5903 receives audio as input, encodes theaudio, and outputs encoded audio as data 5904. A data encoder 5905receives data as input, encodes the data (for example by datacompression), and outputs encoded data as data 5906. Together, theseencoders are referred to as information source encoders 5900.

A transmission unit 5907 receives, as input, the data 5902 of theencoded video, the data 5904 of the encoded audio, and the data 5906 ofthe encoded data, sets some or all of these pieces of data astransmission data, and outputs transmission signals 5908_1 through5908_N after performing processing such as error correction encoding,modulation, and precoding (for example, the signal processing of thetransmission device in FIG. 3). The transmission signals 5908_1 through5908_N are transmitted by antennas 5909_1 through 5909_N as radio waves.

A reception unit 5912 receives, as input, received signals 5911_1through 5911_M received by antennas 5910_1 through 5910_M, performsprocessing such as frequency conversion, decoding of precoding,log-likelihood ratio calculation, and error correction decoding(processing by the reception device in FIG. 7, for example), and outputsreceived data 5913, 5915, and 5917. Information source decoders 5919receive, as input, the received data 5913, 5915, and 5917. A videodecoder 5914 receives, as input, the received data 5913, performs videodecoding, and outputs a video signal. Video images are then shown on atelevision or display monitor. Furthermore, an audio decoder 5916receives, as input, the received data 5915, performs audio decoding, andoutputs an audio signal. Audio is then produced by a speaker. A dataencoder 5918 receives, as input, the received data 5917, performs datadecoding, and outputs information in the data.

In the above embodiments describing the present invention, the number ofencoders in the transmission device when using a multi-carriertransmission method such as OFDM may be any number, as described above.Therefore, as in FIG. 4, for example, it is of course possible for thetransmission device to have one encoder and to adapt a method ofdistributing output to a multi-carrier transmission method such as OFDM.In this case, the wireless units 310A and 310B in FIG. 4 are replaced bythe OFDM related processors 1301A and 1301B in FIG. 13. The descriptionof the OFDM related processors is as per Embodiment 1.

While this description refers to a “method of hopping between differentprecoding matrices”, the specific “method of hopping between differentprecoding matrices” illustrated in this description is only an example.All of the embodiments in this description may be similarly implementedby replacing the “method of hopping between different precodingmatrices” with a “method of regularly hopping between precoding matricesusing a plurality of different precoding matrices”.

Programs for executing the above transmission method may, for example,be stored in advance in Read Only Memory (ROM) and be caused to operateby a Central Processing Unit (CPU).

Furthermore, the programs for executing the above transmission methodmay be stored in a computer-readable recording medium, the programsstored in the recording medium may be loaded in the Random Access Memory(RAM) of the computer, and the computer may be caused to operate inaccordance with the programs.

The components in the above embodiments may be typically assembled as aLarge Scale Integration (LSI), a type of integrated circuit. Individualcomponents may respectively be made into discrete chips, or part or allof the components in each embodiment may be made into one chip. While anLSI has been referred to, the terms Integrated Circuit (IC), system LSI,super LSI, or ultra LSI may be used depending on the degree ofintegration. Furthermore, the method for assembling integrated circuitsis not limited to LSI, and a dedicated circuit or a general-purposeprocessor may be used. A Field Programmable Gate Array (FPGA), which isprogrammable after the LSI is manufactured, or a reconfigurableprocessor, which allows reconfiguration of the connections and settingsof circuit cells inside the LSI, may be used.

Furthermore, if technology for forming integrated circuits that replacesLSIs emerges, owing to advances in semiconductor technology or toanother derivative technology, the integration of functional blocks maynaturally be accomplished using such technology. The application ofbiotechnology or the like is possible.

A precoding method according to an embodiment of the present inventionis for generating a first and a second transmission signal by using oneof a plurality of precoding matrices to precode a first and a secondmodulated signal, the first and the second modulated signal beingmodulated in accordance with a modulation method and composed of anin-phase component and a quadrature component, the precoding methodcomprising the steps of: regularly switching the precoding matrix usedto generate the first and the second transmission signal to another oneof the precoding matrices; and generating the first and the secondtransmission signal, wherein for a first symbol that is a data symbolused to transmit data of the first modulated signal and a second symbolthat is a data symbol used to transmit data of the second modulatedsignal, a first time and a first frequency at which the first symbol isto be precoded and transmitted match a second time and a secondfrequency at which the second symbol is to be precoded and transmitted,two third symbols adjacent to the first symbol in the frequency domainare both data symbols, two fourth symbols adjacent to the first symbolin the time domain are both data symbols, five symbols are precoded withdifferent precoding matrices in order to generate the first transmissionsignal, the five symbols being the first symbol, the two third symbols,and the two fourth symbols, and the second symbol, two fifth symbolsadjacent to the second symbol in the frequency domain, and two sixthsymbols adjacent to the second symbol in the time domain are precodedwith the same precoding matrix used to precode a symbol at a matchingtime and frequency among the first symbol, the two third symbols, andthe two fourth symbols in order to generate the second transmissionsignal.

A signal processing device implementing a precoding method according toan embodiment of the present invention is for generating a first and asecond transmission signal by using one of a plurality of precodingmatrices to precode a first and a second modulated signal, the first andthe second modulated signal being modulated in accordance with amodulation method and composed of an in-phase component and a quadraturecomponent, wherein the signal processing device regularly switches theprecoding matrix used to generate the first and the second transmissionsignal to another one of the precoding matrices, and generates the firstand the second transmission signal, wherein for a first symbol that is adata symbol used to transmit data of the first modulated signal and asecond symbol that is a data symbol used to transmit data of the secondmodulated signal, a first time and a first frequency at which the firstsymbol is to be precoded and transmitted match a second time and asecond frequency at which the second symbol is to be precoded andtransmitted, two third symbols adjacent to the first symbol in thefrequency domain are both data symbols, two fourth symbols adjacent tothe first symbol in the time domain are both data symbols, five symbolsare precoded with different precoding matrices in order to generate thefirst transmission signal, the five symbols being the first symbol, thetwo third symbols, and the two fourth symbols, and the second symbol,two fifth symbols adjacent to the second symbol in the frequency domain,and two sixth symbols adjacent to the second symbol in the time domainare precoded with the same precoding matrix used to precode a symbol ata matching time and frequency among the first symbol, the two thirdsymbols, and the two fourth symbols in order to generate the secondtransmission signal.

INDUSTRIAL APPLICABILITY

The present invention is widely applicable to wireless systems thattransmit different modulated signals from a plurality of antennas, suchas an OFDM-MIMO system. Furthermore, in a wired communication systemwith a plurality of transmission locations (such as a Power LineCommunication (PLC) system, optical communication system, or DigitalSubscriber Line (DSL) system), the present invention may be adapted toMIMO, in which case a plurality of transmission locations are used totransmit a plurality of modulated signals as described by the presentinvention. A modulated signal may also be transmitted from a pluralityof transmission locations.

What is claimed is:
 1. A reception method for receiving a first signaland a second signal precoded and transmitted by a transmissionapparatus, the reception method comprising: receiving the first signaland the second signal, wherein the first signal and the second signalare generated by using one of a plurality of precoding matrices, whileregularly hopping between the precoding matrices, to precode a firstmodulated signal and a second modulated signal modulated in accordancewith a modulation method, the first modulated signal and the secondmodulated signal being composed of an in-phase component and aquadrature component, for a first symbol that is a data symbol used totransmit data of the first modulated signal and a second symbol that isa data symbol used to transmit data of the second modulated signal, whena first time and a first frequency at which the first symbol is to beprecoded and transmitted match a second time and a second frequency atwhich the second symbol is to be precoded and transmitted, two thirdsymbols adjacent to the first symbol in the frequency domain are bothdata symbols, and two fourth symbols adjacent to the first symbol in thetime domain are both data symbols, then the first signal is generated byprecoding the first symbol, the two third symbols, and the two fourthsymbols, the first symbol being precoded with a different precodingmatrix than each of the two third symbols and the two fourth symbols,the second signal is generated by precoding the second symbol, two fifthsymbols adjacent to the second symbol in the frequency domain, and twosixth symbols adjacent to the second symbol in the time domain with thesame precoding matrix used to precode a symbol at a matching time andfrequency among the first symbol, the two third symbols, and the twofourth symbols, the reception method further comprising: demodulatingthe first signal and the second signal using a demodulation method inaccordance with the modulation method and performing error correctiondecoding to obtain data including audio data and generating an audiosignal from the audio data, and outputting the audio signal to an outputterminal, the first signal and the second signal include a controlsymbol, and the reception method further comprising: obtaining controlinformation indicating a modulation method from the control symbol; anddemodulating the data symbols based on the control information.
 2. Areception apparatus for receiving a first signal and a second signalprecoded and transmitted by a transmission apparatus, the receptionapparatus comprising: one or more antennas for receiving the firstsignal and the second signal, wherein the first signal and the secondsignal are generated by using one of a plurality of precoding matrices,while regularly hopping between the precoding matrices, to precode afirst modulated signal and a second modulated signal modulated inaccordance with a modulation method, the first modulated signal and thesecond modulated signal being composed of an in-phase component and aquadrature component, for a first symbol that is a data symbol used totransmit data of the first modulated signal and a second symbol that isa data symbol used to transmit data of the second modulated signal, whena first time and a first frequency at which the first symbol is to beprecoded and transmitted match a second time and a second frequency atwhich the second symbol is to be precoded and transmitted, two thirdsymbols adjacent to the first symbol in the frequency domain are bothdata symbols, and two fourth symbols adjacent to the first symbol in thetime domain are both data symbols, then the first signal is generated byprecoding the first symbol, the two third symbols, and the two fourthsymbols, the first symbol being precoded with a different precodingmatrix than each of the two third symbols and the two fourth symbols,the second signal is generated by precoding the second symbol, two fifthsymbols adjacent to the second symbol in the frequency domain, and twosixth symbols adjacent to the second symbol in the time domain with thesame precoding matrix used to precode a symbol at a matching time andfrequency among the first symbol, the two third symbols, and the twofourth symbols, the reception apparatus further comprising: ademodulation unit for demodulating the first signal and the secondsignal using a demodulation method in accordance with the modulationmethod and performing error correction decoding to obtain data includingaudio data and a signal processing unit for generating an audio signalfrom the audio data, and outputting the audio signal to an outputterminal, the first signal and the second signal include a controlsymbol, control information indicating a modulation method is obtainedfrom the control symbol, and the data symbols are demodulated based onthe control information.